The woman tested positive on Friday after working at Princess Alexandra Hospital and visiting four venues in the city's south on Thursday.

The state government has tested about 230 of the 400 people who may have come into contact with her, but all have come back negative.

"That's great news and we're feeling a little bit relieved today," Premier Annastacia Palaszczuk told reporters on Tuesday.

As a precaution, a lockdown of Brisbane's hospitals, aged care facilities and disability providers has been extended for a further 72 hours.

Meanwhile, guests at the Hotel Grand Chancellor will find out on Wednesday if their quarantine will be extended again.

Some already had to stay for a further three days upon completing their 14-day quarantine period last week after two guests in separate rooms on level one became infected.

One of them passed the virus onto the other, despite having no apparent physical contact, and later to the PA Hospital doctor.

Deputy Chief Health Officer Sonya Barrett said CCTV analysis shows no evidence of a quarantine breach at the hotel.

She said the first guest may be a "superspreader".

"Some people very readily transmit the virus due to a number of factors," Dr Barrett said.

Guests staying on level one have had their quarantine extended for 14 days from March 9.

Hotel staff who worked between March 5 and 9 were tested on Monday, and every guest who left after March 1 has been ordered to isolate and get tested.

Health Minister Yvette D'Ath said 21,861 people have had their initial vaccine shot as of Tuesday morning.

Group 1a, which includes frontline healthcare and quarantine workers, and aged care residents, is set to be fully vaccinated by March 30.

The first vaccine hub on the Gold Coast, and hubs in the Torres Strait, have also started to vaccinate people in group 1b.

Ms D'Ath said that's because the Pfizer vaccine can't be stored after being defrosted, so Queensland Health has been giving doses to other workers if frontline workers aren't immediately available.

"We are having some excess at the end of the day that we're making sure we don't throw in the bin," she said.

The minister said group 1b will be fully vaccinated by mid-June, but she dampened speculation that every Queenslander could be vaccinated by October.

Ms D'Ath said that target isn't possible, with supplies from the Commonwealth only set to ramp up in April.

"Now let's be clear, realistically that's for the first dose, not for being fully vaccinated," she said.

"We are seeing around the world - I don't think we've got to one per cent of the world population yet that is fully vaccinated. This takes time."

Opposition open data spokesman Brent Mickelberg called on the government to publish daily information on how much vaccine is being delivered.

He said they should explain any discrepancies between the rate of supply and the number vaccinations.

"If they've given a reasonable explanation as to why there's been a delay, Queenslanders will accept that, but what they won't accept is being kept in the dark," Mr Mickelberg said.

Queensland reported two new cases in hotel quarantine on Tuesday, unlinked to the Grand Chancellor, with 37 active cases in the state.

Australian Associated Press