The sound of a camel breaking wind travels a long way in the desert. But even so, the long, low and loud reverberating rumble sounds as if it's coming from just behind our tent. We look at each other in alarm: what do you do when a marauding camel invades your camp in the middle of the night?

We're on a rather epic road trip across the western deserts of central Australia and we thought we had all the bases covered. Out here, days away from anywhere, where the tour buses don't venture, you need to be self-sufficient. If there's a problem, it's up to us to solve it. We have a UHF radio and have hired a satellite phone for emergencies. We're carrying enough water to last three weeks, a heavy-duty first-aid kit, snake bandages and a mountain of Tim Tams. We've obtained all the necessary permits to travel remote roads through remote Aboriginal lands, have all the right recovery gear, an air compressor, two spare tyres and a new four-wheel-drive. But what we don't have is a camel contingency plan.

It's midwinter and we'd been dreaming of sunny sand dunes of a different kind: the ones covered in spinifex and poached-egg daisies, flanked by desert oaks and cloaked by a million stars at night. A getaway in every sense of the word, with no email, no phones, no towns and no people. Just endless space where we can empty out our heads.

We're following in the footsteps of one of Australia's legendary surveyors and road makers, Len Beadell, who built more than 6500 kilometres of roads in the centre of Australia through virgin and sometimes unexplored territory to service the Woomera Rocket Range and Maralinga nuclear-bomb test sites between 1947 and 1963.

Our plan is to drive a section of the Anne Beadell Highway, a lonely and deeply corrugated red-dirt track that stretches 1300 kilometres from Coober Pedy to Laverton in the West Australian goldfields, then head north-west beyond Uluru to drive another of his roads, the Sandy Blight Junction Track, between the two Aboriginal communities of Docker River and Kintore.

From the subterranean mining town of Coober Pedy we headed west, out past the opal fields piled high with hundreds of mullock heaps and littered with decaying trucks and machinery, into the Great Victoria Desert. Beadell named the road after his wife, who sometimes joined him, along with their five-month-old baby daughter, Connie Sue, on his road-making trips, although "highway" is a bit of a misnomer - Beadell was well known for his practical jokes.

As we bounce along the sandy corduroy track, we pass numerous survey markers left by his Gunbarrel Road Construction Party - which Beadell called the "Gunbarrel Bush Bashers" - nailed to trees, cemented into rusty 44-gallon drums and half-buried in the red desert sand beside the road, although these days the trademark hand-stamped aluminium plates are replicas, as most of the originals were souvenired years ago.

We're not doing the whole thing, just heading west towards the WA border into Tallaringa Conservation Park, deep in the heart of the Woomera Prohibited Area and just east of Ground Zero, where the British exploded their atomic bombs in the 1950s.

It takes us most of the day to get to the derelict Tallaringa Well, 156 kilometres west of Coober Pedy, and we set up camp in a clearing beside the road, surrounded by clumps of pink everlasting daisies and spindly rings of spinifex that have traced delicate and perfectly circular patterns in the sand as the long spiky shoots wave in the breeze; it's like camping in the middle of the world's biggest Japanese Zen garden, but with camels.

The corrugations have shaken our camp stove to bits, so we teach ourselves how to cook over an open fire, tending the flames at just the right height to cook rather than char. A full moon lights up the desert so brightly we don't even need torches, and we recline our camp chairs and gaze up at a blanket of stars denser than we've ever seen before.

Our second Beadell track, the Sandy Blight Junction Road, is a little more than 1000 kilometres away, via Yulara, but we take the long way there looping up through the Moon and Painted deserts east of Coober Pedy. The well-named Moon Desert is a vast lunar-like landscape that is both dead flat and completely featureless.

The road, which eventually leads to Oodnadatta, spears straight ahead to slip over the horizon, and you can see so far under a sky so big that it's easy to convince yourself that you can actually see the curvature of the Earth. In terms of great Australian deserts, this is one of the smallest, and within an easy day drive of Coober Pedy that you could do in a family car, but we camp out at Arckaringa, a cattle station surrounded by nothing much at all.

The Painted Desert is within its boundaries, and we follow the hand-painted signs to a rather spectacular area of eroded, multicoloured sandy hills that glow red, yellow, ochre and orange in the light of the setting sun.

From there, we bomb it up the Stuart and Lasseter highways towards Yulara. We've both been to Uluru several times before, but the princess in the party (me) decides she's in need of a shower and room service, so we splurge on a pizza and an en suite hotel room. We're probably the only people in Yulara not there specifically to see the rock, but I'm still getting over the shock of paying $280 for a basic room worth $80 in the Outback Pioneer Hotel, the cheapest one-night option at Uluru if you want your own bathroom. Next time we'll try the $150 rooms in the roadhouse at Curtin Springs 85 kilometres down the road.

We can't resist a quick drive out to Uluru the next morning, then head west to Docker River and on to the Sandy Blight Junction Track and into the Gibson Desert. If we thought the Anne Beadell Highway was remote and lonely, this is even more so: it's not a particularly hard track to drive, but you need to have your wits about you because if anything goes wrong, help is a long way away.

Beadell was (in)famous for making his roads as straight as possible (hence the name Gunbarrel) and once said, when asked why, that he "didn't want to make Australia untidy". Every now and then, however, he found a section of the landscape too good to bypass, and one of the highlights of the track is a short detour to Bungabiddy Rockhole, where we follow a faint unmarked walking trail to a beautiful waterhole alive with birdlife. Beadell had stumbled upon this hidden gorge in the Walter James Range while on a reconnaissance, and described it as "an oasis too perfect to conjure up even in dreams" and "decided that wherever else it went, our road would be located as close as possible to this spot".

We spend three days and two nights on the Sandy Blight Junction Track, picnicking under the shade of flowering desert grevilleas, watching great flocks of 20 or more wild camels lope across the landscape and climbing sand dunes at sundown, watching the sunsets paint the sky pink and flocks of budgerigars burst across it all like exploding green fireworks. We set up camp wherever it pleases: one night in the lee of a dune covered in ephemeral daisies, the second on a wide open plain that is also covered in delicate pink, yellow and white desert blooms.

This is one of the most inhospitable landscapes in the country. The track took its name after Beadell contracted the eye disease "sandy blight" during its construction. Lots of people - explorers, gold diggers and adventurers - have died out here, including the desert's namesake, Alf Gibson, who was with explorer Ernest Giles, and Harold Bell Lasseter, of the lost reef of gold fame. At the start of the track we'd climbed up into the cave where Lasseter sheltered for 21 days in the summer of 1931 before he perished in a dry creek bed nearby. Even Beadell, who loved the desert country he spent so much time in, described it as a "parched, forsaken region". It should feel hostile, but with so much vegetation and vast fields of desert flowers, it's like a garden and it feels benign.

This is Aboriginal land - you need to organise permits before you leave home - and it feels like it. The only settlements out here are tiny Aboriginal communities, where we stop to buy fuel and supplies, although fresh vegetables are hard to find (Tim Tams, happily, are readily available wherever we go). You don't hear much English being spoken, and you get the sense that out here nothing changes, not in a hurry anyway, to borrow the words of a once-popular song.

When we later learn that you should always ask the Aboriginal spirits for permission to visit their country or they'll wreak havoc in the form of a fierce wind, we recall the three or four whirly winds that swept across our camp in the Gibson Desert while we were setting up, scattering our gear across the plain, and can't help but wonder whether the spirits were checking us out.

And my partner, who can generally be relied upon to come up with a plan in a time of crisis, has a strategy for coping with camels in the camp.

"Just be cool," he says. "They'll know we're nice." The logic's a bit lame, but it seems to work.

Trip notes

Getting there

Tallaringa Conservation Park is 615 kilometres north-west of Port Augusta, and Tallaringa Well is 156 kilometres west of Coober Pedy, via the Anne Beadell Highway. The track is narrow in places, rough, deeply corrugated and definitely 4WD only.

The Moon Desert is a short drive east of Coober Pedy; Arckaringa and the Painted Desert is about 150 kilometres, via the Oodnadatta Road. The road is suitable for conventional cars, although a 4WD or SUV is recommended for the Painted Desert.

The Sandy Blight Junction Track from Docker River (Kaltukatjara) to Kintore (Walungurru) is 331 kilometres — Docker River is 230 kilometres west of Yulara (Uluru), Kintore is 522 kilometres west of Alice Springs. The track isn't difficult, but there are some low sand dunes to crest, corrugations and it is a 4WD-only route.

When to go there

Do not attempt these tracks in summer, when temperatures can climb beyond 50 degrees. Winter, when daytime temperatures are pleasant (although nights are very cold) and the flies are elsewhere, is the best time to go.

Before you go there

You'll need a Desert Parks Pass to visit Tallaringa: environment.sa.gov.au/parks/Park_Entry_Fees/Parks_Passes.

You need an NT permit from the Central Land Council to travel on the Great Central Road (Uluru-Docker River) and the Gary Junction Road (Kintore-Papunya) plus a West Australian permit from the Department of Indigenous Affairs for the Sandy Blight Junction Track. clc.org.au/articles/info/transit-permit-application; dia.wa.gov.au/en/Entry-Permits.

Satellite phones: mobile phone access is non-existent in the outback. Hire a satellite phone so you can call for help if needed — as long as there is a clear line of sight between the satellite phone's antenna and the sky, you can make calls. Some tourist information centres in remote areas have satellite phones you can hire. satellitehire.com.au, rentasatphone.com.au.

Camping there

You can bush camp anywhere in cleared areas within 50 metres of the road along the Sandy Blight Junction Track and in Tallaringa Conservation Park.

Arckaringa Station offers unpowered campsites with hot showers for $20 a vehicle. thepainteddesert.com.au.

More information

Hema's Great Desert Tracks Atlas and Guide, by Ian Glover & Len Zell, is available at most bookshops or from wilddiscoveryguides.com.

Outback Highways by Len Beadell offers a humorous insight into the trials and tribulations of outback road building, including the Anne Beadell and Sandy Blight Junction Tracks. beadell.com.au.

The trip was self-funded.