The storm hit the state's most populous region on Thursday after pummelling the north-east coast for two days.
Although no longer a cyclone, the storm has lashed Queensland's capital Brisbane with 200mm of rain in two hours - more than its monthly average.
No injuries have been reported, but authorities closed more than 1,000 schools and urged people to stay home.
"We have not seen the worst of this weather system in the south-east," said Queensland Premier Annastacia Palaszczuk.
Every school in an almost 600km (370 miles) area stretching from Agnes Water to Coolangatta will remain closed until at least Monday, she said.
Prime Minister Malcolm Turnbull surveys the cyclone damage from a military helicopter
Queensland Police Commissioner Ian Stewart said the "unprecedented late call" was made after some children were already at school.
"We can't afford to have inexperienced young kids walking home from school at a time where there could be flash-flooding," he said.
More than 1,200 childcare centres were also closed, according to a government website.
Authorities pleaded with people to stay off roads and close shops, saying dozens of people had been rescued from floodwaters.
Rescues under way
Queensland Fire and Emergency Services Commissioner Katarina Carroll said it was "extraordinary" there had not been more injuries, criticising one person seen on a jet ski.
"What our worst fears are is that people do silly things like this, and this is when the tragedy will occur," she told the local Nine Network.
"Please keep your children away from drains [and] stay in your house."
A satellite image of the storm system over south-east Queensland
Authorities warned flash-flooding is highly unpredictable
Australia's Bureau of Meteorology said parts of south-east Queensland could see up to 400mm of rain on Thursday.
"What we know is that we are anticipating the heavy falls in a short duration of time," senior forecaster Matthew Bass said.
Prime Minister Malcolm Turnbull said nature was "flinging her worst" at Australians.
"It is going to take some time to recover, and that's why we are here to show our support and commitment," he said from Bowen, a damaged town in northern Queensland.
Cyclone Debbie made landfall in north-east Queensland as a category four system on Tuesday.
Authorities said 61,000 homes remained without power, and there was major damage to buildings, sugar cane and tomato crops.
The cyclone is also likely to have damaged the Great Barrier Reef, marine experts warned.