Health Minister Yvette D'Ath says the new case is linked to the existing cluster south of Brisbane and was in quarantine during their entire infectious period.

Meanwhile, the state's vaccination centres are welcoming walk-ins for the first time, with reports of lines forming as early as 4am on Saturday.

"I'm already hearing some of our sites are hitting capacity, so the Logan Entertainment Centre (is) currently cutting off their walk-ins and redirecting people to other sites," Ms D'Ath said.

She said those hoping to get jabbed without an appointment would be updated as to whether they should return another day or go to a different site.

"Look at some of those smaller hubs, not just our big ones," she said.

"It is a warm day out there ... so please bring a hat, some water, maybe some sunblock if you're going to be standing in those lines."

For those who miss out, chief health officer Jeannette Young says walk-ins will be welcomed to vaccination hubs on coming weekends.

"Maybe not everyone will get the chance this weekend because the turnout has been unbelievable, far more than I ever hoped for," she said.

Queensland's vaccination rate has just tipped over 40 per cent for those receiving two jabs, marking the half way point of the state's 80 per cent target.

Australian Associated Press