Pat Henshall, 96, became the first patient at Flora Hill Medical Centre to be administered the vaccine.

She made the booking at the suggestion of her doctor.

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"I think it's something we have to have to get us out of this," she said of the vaccine.

While she wasn't fond of needles, she was "quite confident" ahead of the jab.

The Flora Hill Medical Centre was one of a number of GP clinics in the Bendigo area known to be administering COVID-19 vaccines in the first week of the phase 1b rollout.

The medical centre received 80 doses of the vaccine, with the hope of a further 100 next week.

"We have already got 80 people booked for this week," Dr Mario Fernando, of the Flora Hill Medical Centre, said.

"For the first week we are booking everybody over 80 up to the late 90s."

Thirty-two people were booked for vaccinations on Tuesday, the medical centre's first day administering the jabs.

Most of the Bendigo GP clinics known to be involved in the first week of the phase 1b rollout gave their first vaccines on Tuesday.

A GP clinic in Kangaroo Flat is known to have started administering jabs on Monday, when phase 1b started nationally.

More than six million Australians are eligible to be vaccinated as part of the latest phase of the vaccine rollout.

They include adults at or over the age of 70, Aboriginal and Torres Strait Islander people over the age of 55, and people with specific medical conditions and disability.

Health care workers and critical and high-risk workers are also eligible in phase 1b.

Tristar Medical Centre Epsom received about 300 phone calls in two days from people seeking to make bookings as part of the phase 1b rollout.

The clinic had to reschedule some of the patients who had been booked for week one vaccinations because it only received 80 doses.

Staff were hopeful the next supply would consist of 100 doses.

More than 50 patients were scheduled for jabs on Tuesday, the first day Tristar Medical Centre Epsom had been administering the vaccine.

Centre staff believed some clinics had been awarded as few as 50 doses a week.

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Tristar Medical Centre Epsom nurse immuniser Helen Heaney said the rollout had been good.

She urged the community not to be frightened of getting vaccinated.

Dr Fernando also reassured the community the vaccine was safe.

"The vaccine has been very well tried and tested and gone through all the different phases of clinical trials, as with any other medication... or vaccine," he said.

While he conceded no medication was free of a reaction, Dr Fernando said it would be a very rare occurrence.

European and Australian experts had confirmed reports of blood clotting were not directly linked to the vaccine, Dr Fernando said.

To check your eligibility as part of Australia's COVID-19 vaccine rollout, click here.

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