Young children can now be vaccinated against COVID-19, with the first five-to-11-year-olds receiving their initial dose on Monday.
An estimated 2.3 million children in the demographic are now eligible for the Pfizer vaccine, with three million doses being distributed across the country.
Prime Minister Scott Morrison said he was confident the vaccine rollout for children would be managed well and doses would be freely available.
"There are 6000 places where people can go (for a child vaccination)," the prime minister told reporters in Canberra on Monday.
"There are 835,000 vaccines in those places right now as of last Friday and more would have been added to that since then - if you can't get it from where you would normally go, know there are other places where the vaccines are on the shelves."
The Pfizer vaccine for five-to-11-year-olds is being distributed in orange-capped vials to differentiate it from other vaccines and will be given in two doses at least eight weeks apart.
The government is hoping children will receive their first dose of the vaccine before schools resume at the end of January.
However, Queensland has delayed its start of the 2022 school year due to rising virus cases from the Omicron variant and to allow more time for children to be vaccinated.
Despite the child vaccine rollout beginning, some GPs say their allotment of vaccines has yet to arrive, with many forced to cancel vaccination appointments.
The head of Australia's vaccine rollout Lieutenant General John Frewen conceded he would not be surprised if there were minor concerns about bookings with millions of children becoming eligible on the same day.
"There is a lot of people getting vaccines very quickly right across the country so I encourage a little bit of patience and a little bit of persistence and I have no doubt they will get access to vaccines in the week ahead," he told reporters in Canberra.
Royal Australian College of General Practitioners president Karen Price said urgent action was needed to ensure children got vaccinated.
"We must ensure that vaccine supplies reach practices so that GPs and general practice teams can get on with the job of vaccinating our children," she said on Twitter.
"With term one of school fast approaching, action is needed."
Opposition Leader Anthony Albanese said the delays in vaccines arriving at clinics were causing frustration for parents.
"This is causing enormous pressure on families, enormous concern from parents who just want their children to be kept safe," he told reporters in Townsville.
"It's also enormous pressure on people who just want to get their booster shot."
The latest vaccination data showed 85,967 booster shots were administered nationally on Sunday.
There are now 3.6 million people who have received their third vaccine dose.
More than 60 per cent of eligible people had received their first dose before the timeframe between shots was brought forward to four months on January 4.
The prime minister encouraged Australians to get vaccinated as he admitted the Omicron variant had spread faster than anticipated.
"Its rate of escalation has been very strong and that has been moving at a very quick rate compared to our early estimates," Mr Morrison said.
"(But) what we've also seen is the severity of it being far less than perhaps was anticipated."
It comes as Australia on Monday surpassed one million total COVID-19 cases since the pandemic began two years ago.
Of the total cases, one-quarter of those came from just the last four days alone.
There were more than 71,000 new cases of COVID-19 that were reported across the country on Monday.
NSW reported 20,293 new infections along with 18 deaths, while Victoria recorded 34,808 new COVID-19 cases and two deaths from the virus.
There were also 9581 new infections in Queensland, 1218 in Tasmania, 938 in the ACT and 404 in the NT.
South Australia had 4024 cases, while Western Australia had eight infections.
Australian Associated Press