The first week of vaccinations was marred by two elderly patients in Brisbane being hospitalised after they were administered four times the recommended dose.

Up to 150 doses of the Pfizer jab were thrown out in Victoria after concerns they had spoiled through not being refrigerated properly.

State governments have criticised the federal government's distribution of doses and some nursing home residents waited for vaccines that didn't show up.

Department of Prime Minister and Cabinet secretary Phil Gaetjens criticised attention on the problems.

"I would put those issues in the category of noise," he told the Senate's coronavirus response committee on Tuesday.

"Above that, there is a very strong signal that the vaccine is going out OK."

Labor senator and committee chair Katy Gallagher said the problems were serious, describing the hospitalisations as traumatic.

"You've got to accept an overdose in terms of confidence with the vaccine rollout, kicking off with overdosing two elderly Australians, isn't really an optimal outcome," she told Mr Gaetjens.

"That's not really just noise."

But the head of Scott Morrison's department downplayed the concerns as teething issues that were expected during a massive logistical effort.

"The more that people go on about small issues like this, that affects confidence more than the actual impact of those small issues themselves," he said.

While conceding it shouldn't have happened, Mr Gaetjens questioned how the Brisbane overdoses could have been prevented.

The company contracted by the government to provide vaccination staff has admitted the doctor was untrained in administering the Pfizer jab.

Senator Gallagher argued the overdoses could have been prevented if proper training was linked to doctors' registration for the rollout.

The prime minister is confident all Australians who want a vaccine will have access to at least one dose by the end of October despite delays.

"That doesn't mean we won't hit some obstacles," Mr Morrison told reporters in Sydney.

"It doesn't mean there won't be the odd frustration, the odd logistics issue that needs to be addressed. That's to be expected with a project of this scale."

More than 86,000 people had received their first injection as of Sunday, which marked the second week of the rollout.

While the program was always designed to ramp up as it progressed, the government now needs to dramatically increase administration to reach its goal.

The prime minister expects the figure to break 100,000 this week, fuelled by supplies of overseas-produced vaccine.

Mr Gaetjens is also working with state and territory counterparts to provide advice to leaders about how changing risks could lead to coordinated approaches on restrictions.

Nationals senator Perin Davey, who is based in Deniliquin near the NSW-Victoria border, said there was major anxiety about the prospect of snap travel restrictions.

Mr Gaetjens said his work was about providing data to show measures that had been used previously may not be necessary.

Australian Associated Press