Among the centres that started the rollout were the Worrigee and Vincentia Medical Centres.

Practice principal and nurse at the Vincentia Medical Centre Annette Pham said she was thrilled to have phase 1b of the vaccine begin.

"We have been anticipating this day for quite some time and we're just super excited and ready to go," she said.

"We don't have enough COVID vaccine supply just yet to suit everyone's needs, so people need to be kind and patient and remember their time will come."

Included in the phase 1b rollout are:

Around 35 people were vaccinated at the Worrigee Medical Centre, and 16 were vaccinated at the Vincentia Medical Centre.

While supplies are limited at the moment, the Therapeutic Goods Administration approved the domestic production of the Oxford-AstraZeneca vaccine on Sunday.

"We have limited supply at the moment, we have something like 15,000 patients within our practice in that 1b category," said Mrs Pham.

"And so at 650 doses a week, it's going to take us quite some time. But we are expecting to have a much greater supply."

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Mrs Pham said the best way to book was with your regular general practitioner via hotdoc.com.au.

"That's the the easiest, most convenient way to do your consent forms online. You get information about the vaccine, it asks you relevant questions, so that if there's any queries, it will ask you to go and perhaps see your doctor first," she said.

Mrs Pham reassures that the vaccine is safe.

"It is a perfectly safe vaccine," she said.

"It's going to give us all our lives back. If people aren't vaccinated then the spread of the virus can still happen, and people who are most vulnerable will be the most affected."

With the practice being inundated with calls, Mrs Pham said the logistics of the rollout will become smoother as more people are vaccinated.

"I would just like to say a great big thank you to our wonderful GPs and nurses and reception staff, who have worked really hard to get the vaccine rolled out to our patients and to the primary health care network coordinator. And also to everybody involved. It's a big logistical exercise."

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