Two people have already died in floods triggered by the system - a 54-year-old man was killed trying to ride a motorbike through rising water at Gympie and a 63-year-woman was found dead in a submerged car on the Sunshine Coast.
The Bureau of Meteorology has issued a "very dangerous thunderstorm" alert for residents in the Gympie, Somerset, Sunshine Coast and Noosa areas for Friday.
The forecaster warns intense rain from the slow-moving system could put people living in Kenilworth, Eumundi, Mapleton, Yandina, Conondale, Nambour and the area west of Conondale at risk.
"Intense rainfall that may lead to dangerous and life-threatening flash flooding is likely," the BoM said in its alert.
Queensland Fire and Emergency Service Deputy Commissioner Mark Roche said his organisation had made more than 30 flood rescues and responded to 100 calls for help overnight.
"It's a busy time for our staff and volunteers," he told Nine's Today program on Friday.
"I don't know the details of all of the incidents, but I would suspect that people are not listening to the message: 'If it's flooded, forget it'.
"People are possibly getting surprised by the water on the roadway, but with this weather, people should be prepared."
The Department of Transport said flash flooding had cut dozens of roads in Brisbane, Bundaberg, the Darling Downs, the Gold Coast Hinterland, Gympie, Ipswich, Moreton Bay, Noosa, the Sunshine Coast and its Hinterland, Toowoomba.
A large trough has been battering the state's southeast, mostly areas north of Brisbane, causing flash floods and moderate flooding for almost four days.
The BoM said an area north of Biggenden recorded 423mm of rain in the 24 hours to 5am on Friday, with 389mm falling in just four hours.
The BoM has also issued a severe thunderstorm warning for parts of Wide Bay and Burnett, and Darling Downs and Granite Belt districts.
More intense rainfall, floods and damaging winds are expected on Friday and into Saturday as the storm pummels large parts of the southeast.
Six-hour rainfall totals between 80mm and 120mm are likely, with falls of up to 300mm possible north of Brisbane.
"Locally intense rainfall leading to dangerous and life-threatening flash flooding is possible with thunderstorms during this period, particularly over areas north of Brisbane," the BoM said.
The forecaster has also warned of damaging winds with gusts of potentially more than 90km/h from the town of Seventeen Seventy to Brisbane.