Health Minister Greg Hunt is confident the nation will move to the next phase of the vaccine rollout in six weeks.
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More doses of the Pfizer coronavirus shot have arrived in Australia as the early stages of the rollout continue.
Labor leader Anthony Albanese and Greens leader Adam Bandt have received their first dose in Canberra, in a bid to boost public confidence.
Labor MP Peta Murphy, who has metastatic breast cancer, also got the vaccine.
"I wouldn't ask anyone to do something I'm not prepared to do," she later posted to Twitter.
"If you have concerns, talk to your treating doctors. I did and I am confident it is safe to take the vaccine.
"Do it for yourself, do it for the community."
South Australian Premier Steven Marshall also received the jab, saying it was a show of confidence in its safety.
"We can't expect other people in the community to have the vaccine if we're not prepared to do it ourselves," he told reporters on Tuesday.
Frontline health and hotel quarantine workers across the country have begun receiving the vaccine, along with aged and disability care residents and staff.
Prime Minister Scott Morrison received the Pfizer vaccine on Sunday.
Mr Hunt confirmed on Tuesday another 166,000 doses of Pfizer have landed in Sydney, with another 120,000 to arrive next week.
He told parliament the government planned to ensure 80,000 doses would be made available next week - 50,000 going to the states and 30,000 for aged care.
"All of this is part of phase 1a - we will soon move after approximately six weeks to phase 1b," the minister said.
The next phase provides vaccinations for the over-70s, people who are immuno-compromised, Indigenous people over 55 and critical frontline workers.
Mr Morrison also expressed confidence to MPs in the coalition party room.
"Every day from here gets more normal," he told colleagues.
"It may have been a crap year but it's time to get excited. Australia is shining in a way that the rest of the world can see."
Mr Morrison compared the situation to navigating the Kokoda track.
"You wonder how you've got over the first hill and the next one's even bigger. That's what it's like in the pandemic," he said, citing the next hill as being weaning the economy off government support.
Australia has recorded 26 days of zero local cases so far this year, including six of the past seven days.
Authorities are now looking at how and when restrictions can be eased.
Expectations are rising more Australians will be allowed to return home from overseas in coming months as the vaccine rollout progresses.
About 40,000 Australians are seeking to return but arrival caps and limited quarantine capacity mean they cannot do so.
Chief nurse Alison McMillan is in the Northern Territory for discussions on a further expansion of the Howard Springs facility outside Darwin.
The federal and Queensland governments are also looking at the potential for a purpose-built quarantine facility in Toowoomba.
However Queensland Premier Annastacia Palaszczuk said on Tuesday the federal government was holding up the project.
"This is just ridiculous - the departments are talking at length about these issues and it makes logical sense," she told reporters.
"The federal government should just get on with it."
Australian Associated Press
