Deputy Chief Medical Officer Michael Kidd said more appointments would become available in the coming weeks as more facilities join the rollout, which began on Monday.
"We have enough of the paediatric Pfizer vaccine for every five to 11-year-old to receive their first dose by the end of this month," he told the ABC on Tuesday.
"There is no need to panic. There will be appointments available over the next couple of weeks before children are starting to go back to school in Australia."
Labor health spokesman Mark Butler said there were cancelled appointments because GPs were not getting vaccination supplies as promised.
"Parents want a solid commitment from the prime minister that their children will have access to a vaccine before school returns later this month and that's a very reasonable expectation," he told the ABC on Tuesday.
But as children face starting the school year unvaccinated, a leading epidemiologist says young school children should be taking rapid antigen tests "every other day" to minimise the risk of a breakout.
With the time to the second dose sitting at eight weeks, Professor Mary-Louise McLaws says schools face an enormous transmission risk as children won't begin to be fully vaccinated until mid-March at the earliest.
"So they should be really using rapid antigen tests at least every other day when they are going on to the school site because there could be - unknown to everybody - infected and unvaccinated (children)," she told the Nine Network on Tuesday.
"Therefore, all kids could be at risk."
Prime Minister Scott Morrison has ruled out making RATs free across the board.
But speaking ahead of the last national cabinet, ACT Chief Minister Andrew Barr said free RATs in schools was on the agenda and "I think even the prime minister is on board in that context."
Mr Morrison said plans for the return to school in the coming weeks would be worked through during talks this week.
The country's chief medical officer Professor Paul Kelly said health-based issues would be taken into account before a unified approach was decided.
The federal government is also working through supply chain problems after distribution staff shortages resulted in a lack of goods in supermarkets.
Deputy Prime Minister Barnaby Joyce said the country has not run out of food but Australians needed to "cool their heels a bit" and act rationally as Omicron continues to spread.
"We have to stop hoarding stuff, take what you need not more than what is required," he told Sky News.
"The food is there, we are not going to run out of food. What we will run out of is common sense if people start running in and swiping everything off the shelves because they think were going to Armageddon."
Meanwhile, unions are calling for an urgent meeting with the government to discuss the impact of the spread of the Omicron variant on exhausted essential workers.
Australian Council of Trade Unions Secretary Sally McManus wrote to Mr Morrison overnight with a list of demands warning an "unofficial lockdown" was hurting affected workers.
"The prime minister has not heard from working people and we are on the front lines," Ms McManus said in a statement on Tuesday.
"Australian workers are not OK at the moment. We have never had so many working people sick at once.
"Healthcare workers are exhausted, people are anxious and uncertain."
The demands include the restoration of pandemic leave for workers who are close contacts of infected colleagues, rather than just household contacts.
Australia on Monday passed one million COVID-19 cases since the pandemic began two years ago.
Of that total, one-quarter were recorded in the past four days.
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