The news comes as the premier also announces that the state's next vaccination hub will open this Wednesday, September 8.
The facility will be at the Brisbane Entertainment Centre at Boondall and will work in conjunction with the existing hub at the Convention and Exhibition Centre.
"We're pleased to announce that from September 8, we will be opening up another big vaccination hub," Ms Palaszczuk said.
"It will open up to its first 1500 bookings and we'll ramp that up to 3000 a day.
"So, if you're living on the north side and you're thinking 'hey, now's the time for me to get my vaccine, you'll be able to go and do that at Boondall in just over a week and a half."
On the new local case in the state, Ms Palaszczuk said that they are a family member of a previous infection and they had not been active in the community.
"They're in home isolation, it's part of the Indooroopilly cluster and it's the last person of a particular family.
"We have absolutely no concerns about that".
Asked on what is being done to assist with the ongoing issues with stranded communities along the joint NSW-Queensland border, Ms Palaszczuk said she's "trying her hardest".
"Look, I've tried," she said.
"I'm trying. We're trying our hardest, so let's hopefully see what happens with the discussions with NSW border commissioner and our state disaster coordinator.
"I think we've sent one of our best, and everyone knows how good our deputy commissioner is, if anyone can get it done, he can."
The Queensland border is currently closed to all people from NSW, save for a small handful of essential workers, creating chaos for families and businesses in the towns of Tweed and Coolangatta.
Some residents were given as little as two hours notice to get across the border when the initial lockdown announcement was made, with many now forced to take up residences at temporary accommodation facilities such as caravan parks.
NSW and Queensland governments are in talks about moving the interstate border south, however no conclusive action has so far been taken.