The state government is offering free vaccines to head off a projected rise in hospitalisations from an outbreak of influenza A, which reached 4282 cases on Monday.
Ten people are in intensive care and 151 are in hospital for the acute form of flu, which hasn't broken out in Queensland for five years.
Some GP clinics have complained about a lack of jab supplies amid a surge in demand, and called for special vaccine hubs.
Health Minister Yvette D'Ath is reluctant to set up jab hubs, saying it will take health workers off the front line when public hospitals are already facing capacity pressures.
"I just don't believe that's the most appropriate thing to be doing right now when we need them in our EDs (emergency departments) and in our hospitals dealing with the patients that we have," she told ABC radio on Tuesday.
The minister said the government was open to the idea of hubs, but at the moment GPs and chemists were the best placed to administer the flu jabs.
Australian Medical Association Queensland (AMAQ) president Chris Perry agreed that setting up flu vaccine hubs would put more pressure on public hospitals.
"The minister has got her head all around it - it's best to go through the GPS and the pharmacies, and hopefully that'll be a successful program," he told ABC radio.
"If you do have hubs forming it's going to take people away from hospitals."
Dr Perry called for calm after some people rang GPs and abused them for not having jabs ready on Monday afternoon, saying vaccine supplies might take up to a week to get to some remote GP clinics.
Ms D'Ath denied the government had taken too long to act. It had been calling for Queenslanders to get vaccinated since the start of the year, she said.
The minister stressed the major issue with the influenza A outbreak was that fewer people had been vaccinated for flu this year than in previous years.
Just more than half of people aged over 65, six per cent of children aged six months to five years, and 14 per cent of six- to-64-year-olds have had the jab.
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