The driver was infectious in the community in Archerfield and Mount Gravatt, in southern Brisbane, on Sunday and Monday and tested positive in NSW after returning from Queensland.

A public health alert is being issued for contact tracing locations in Archerfield and the Westfield Garden City shopping centre in Upper Mount Gravatt

The government is asking Queenslanders to monitor the list of exposure venues on the Queensland Health website and follow the public health advice, as there may be more locations.

It is the second locally acquired case of COVID-19 the state recorded on Thursday after the brother of a four-year-old girl who has coronavirus also tested positive in Queensland.

However, authorities believe the risk to the community is low.

Premier Annastacia Palaszczuk says the boy's positive result came after a total of 13,516 tests were conducted in Queensland in the 24 hours to 6.30am on Thursday.

He caught the virus from his four-year-old sister in home quarantine, with both cases linked to the Beenleigh cluster centred on a school, a daycare centre and a shopping centre south of Brisbane.

"So absolutely no concerns about that," she told reporters on Thursday.

Chief Health Officer Jeannette Young said the boy posed no risk to the community because he had been in home quarantine for his entire infectious period.

Another 99 families linked to the Beenleigh cluster, which has now risen to four cases, are also in home quarantine.

The prime minister had high praise for NSW Premier Gladys Berejiklian on Thursday after she detailed her state's road map out of lockdown. It will begin at 70 per cent double-dose vaccination coverage, a milestone expected in mid-October.

Scott Morrison said he was looking forward to other states following suit, telling premiers to prepare their hospitals for the inevitable pressures reopening will bring and urging them to hold their nerve.

Not long afterwards, Deputy Premier Steven Miles said Queensland would keep its borders shut for now, despite NSW's plan to lift lockdown orders in 13 of the 16 local government areas along the border on Saturday.

Those 13 areas have not recorded any cases in the past fortnight.

"The Queensland border restrictions remain in place," Mr Miles told AAP.

"I have spoken to the NSW Deputy Premier (John Barilaro) today and we agreed the (NSW) Cross Border Commissioner and Queensland's Disaster Coordinator should meet to discuss the new arrangements in northern NSW."

A special exemption allowing locals on both sides of the border to work, go to school or university, obtain healthcare or to provide care has been on hold since July 23.

At present, only certain essential workers who have had at least one dose of a COVID-19 vaccine are allowed to cross into Queensland from NSW.

Meanwhile, the premier has suggested more staff could be hired to work in the exemptions unit, which assesses whether people who are not essential workers are allowed into Queensland's hotel quarantine on medical or compassionate grounds.

The government has been criticised numerous times for failing to give people interstate exemptions to be with dying relatives in Queensland, and for leaving its own residents stranded interstate.

Ms Palaszczuk said the exemptions unit was trying to show people compassion while keeping the virus out of Queensland, but admitted more could be done including beefing up staff numbers.

"It's a balancing act," she said.

"I've spoken with the health minister, I've spoken with the D-G, and the Director General is under no illusions that I expect there to be more done in this area, and if we need more people, we will get more people."

Queensland Health delivered 23,889 vaccine doses on Wednesday, with 54.28 per cent of eligible Queenslanders having had one dose and 35.81 per cent fully vaccinated.

The Townsville, Mackay and Rockhampton vaccine clinics are now accepting walk-ins.

Australian Associated Press