Twenty-four hour rainfall in some areas had exceeded 300mm.
The greatest risk on Thursday afternoon was in the Moreton Bay region, with flash flooding at creeks in the area affecting at least 25 roads, Queensland Police state disaster co-ordinator Chris Stream said
"We just need to be people to be really cautious," he said.
An ABC reporter and a bystander swam to rescue a trapped man before his car completely submerged.
"Had those people not intervened … there's every chance that fellow would have died," Mr Stream told AAP.
"The car was three-quarters submerged, just the back end was tipping up, and luckily they were able to get to him and pull him out."
Caboolture received 240mm on Thursday morning and Moorina had 206mm, which was "a ton of rain to fall in a six-hour period anywhere in the country", the Bureau of Meteorology's Angus Hines said.
There was also 231mm at Morayfield, north of Brisbane, where a driver was rescued from his sinking vehicle.
The electrical systems on modern vehicles created additional risk, because water could prevent windows from opening and water pressure could prevent doors from opening, he said.
Firefighters used a raft to retrieve an elderly man who was clinging to the roof of his vehicle at Caboolture.
At least two other swift-water rescues had been performed by members of the public.
A truck driver drove into floodwaters at Goondiwindi and plucked a stranded driver from his vehicle, and another driver at Petrie had been rescued by community members.
Rescue crews had been called to nine incidents since 11pm on Wednesday, but the vehicle occupants had either self-extracted or been rescued by the public, QFES state co-ordinator Doug May said.
Extra rescue crews were on stand-by through until Monday, when severe storms were again forecast, with the risk of hail.
The Bureau of Meteorology said heavy rainfall from severe thunderstorms had caused flash flooding across the southeast, and Caboolture residents were warned to prepare to leave as floodwaters rise rapidly.
Meteorologist Robert Urbaniak said the region was "definitely not out of the woods yet".
Caboolture resident Sara Wessling said the flash flooding on Thursday morning was the worst she had seen.
"I had just walked over to have a look at how deep it was getting and saw an older guy flashing his head lights as he had driven into the water not realising how deep it was," she said.
She called triple zero and emergency services arrived quickly.
"Another small four-wheel drive drove straight into it and ended up needing help as well - as far as I know all the people in both vehicles were fine."
The weather system was affecting the Sunshine Coast and parts of Brisbane, from Maroochydore through to Ipswich, and rain would persist throughout the day, particularly for the Sunshine Coast.
At least a dozen schools across the region were closed.
Parts of the Moreton Bay council area received more than 100mm in three hours, resulting in flash flooding.
Mr Urbaniak said the weather conditions were the perfect storm.
"Because the winds are quite slow coming off the ocean, and the winds through the first few kilometres of the atmosphere are quite slow, that means the storms are slow moving, so that's what's making it worse," he said.
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