The state government is furious and says it is farcical for the Morrison government to claim borders are closed when it let in 20,000 non-Australians last month alone.

It has also warned it's running out of the Pfizer vaccine but is refusing to recommend younger Queenslanders seek AstraZeneca after the prime minister announced anyone under 40 can ask their GP for it.

During a fiery press conference on Wednesday, Premier Annastacia Palaszczuk and her deputy Steven Miles savaged the federal government for letting an unvaccinated traveller make repeated trips between Australia and Indonesia.

That traveller wound up in Brisbane's Prince Charles Hospital with the highly infectious Delta variant and passed it to a young receptionist, who should have been vaccinated but wasn't.

The receptionist was then active in the community for 10 days while infectious. In that time she continued to show up for shifts at the hospital and she and her family took a holiday to Townsville and Magnetic Island.

On Wednesday, authorities said her younger brother was among three new cases of community transmission in Queensland. Contact tracers are now scrambling to work out if the boy infected others at a school holiday tennis camp at the Wooloowin tennis centre.

Mr Miles says the federal government is letting in thousands of people "who are not stranded Aussies", and is also allowing thousands of other Australians to leave and then return for business and other non-critical reasons.

"It's not good enough," he told reporters.

"We need to reduce the number of people travelling overseas, and back into the country, the number of people coming into the country with COVID, until we have higher vaccination rates and dedicated quarantine facilities."

Health Minister Yvette D'Ath faced a barrage of questions about why the hospital receptionist was allowed to show up for shifts just outside the COVID ward without being vaccinated.

"Someone has failed here, yes," she said.

She insisted the woman should have been vaccinated but also accepted health directives relating to vaccinations for frontline workers might have grey areas that would be tightened.

The premier lashed out at Scott Morrison's announcement that Australians can seek the AstraZeneca vaccine from their GPs regardless of age, telling Queenslanders to take their advice from Chief Health Officer Jeannette Young.

Dr Young told reporters she didn't understand the prime minister's "thought processes" on AstraZeneca, and remains strongly opposed to allowing younger people to have it due to an extremely rare risk of a blood clotting disorder.

"No, I do not want under 40s to get AstraZeneca, because they are at increased risk of getting ... that rare clotting syndrome."

The health minister said Queensland has about eight days of Pfizer stock left and despite a request had been denied extra.

She warned authorities might soon have to start prioritising second doses unless the Commonwealth comes to the party.

Two other cases of community transmission were reported in Queensland on Wednesday.

One is a person linked to the Alpha variant cluster at a Portuguese restaurant at Ellen Grove. That cohort has been isolating so the risks are considered low.

The other is a close contact of an infected Virgin Australia flight attendant who flew on services to Brisbane and the Gold Coast, and who has also been in isolation.

Contact tracers are working to determine if they had any public exposure before being placed into quarantine.

Queensland's partial lockdown covers residents of Brisbane, Ipswich, Logan City, Moreton Bay, Redlands, the Sunshine Coast, Noosa, Somerset, Lockyer Valley, Scenic Rim, the Gold Coast, Townsville, Magnetic Island and nearby Palm Island until 6pm on Friday.

Australian Associated Press