Destructive winds gusting to 60 knots are also expected.
Forecasters are expecting conditions "comparable to a high category one cyclone" with wind gusts of 60 knots, or 125kph, in the southeast corner over the next day.
The low pressure system is expected to be over the Sunshine Coast this afternoon, Brisbane by this evening, and the Gold Coast by late on Sunday night or early on Monday.
It will then move across the border into northern NSW.
The bureau's Queensland weather services manager Richard Wardle says there's a strong chance of more tornadoes like the six that caused severe damage in the Bundaberg region on Saturday and Sunday.
In the state's southeast corner, falls of between 200 and 300mm are expected but that could reach 400mm in some locations, Dr Wardle said.
The central Queensland cities of Gladstone, Bundaberg and Gympie are all experiencing widespread flooding.
There have been dramatic rescues across the region, including in Gympie where the mayor says people had been rescued from rooftops.
There are grave fears for at least one man who remains missing after trying to cross a flooded creek near Gympie on Sunday morning.
Residents of north Bundaberg are being ordered to leave their homes immediately, the ABC reported at midday (AEST), with fears 300 homes will flood and those that don't to be left isolated.
Some residents in south and east Bundaberg also being told to leave, the ABC said.
The Queensland government has asked for army helicopters to be sent in to help, the ABC reported.
And Premier Campbell Newman has called on Prime Minister Julia Gillard to say the state will need help to deal with a crisis spanning many communities simultaneously.
Mr Newman said it was highly likely the army would be called on for more support, particularly in the clean-up phase.
"I know she and her government will provide the support we need," Mr Newman told reporters in the tornado hit community of Bargara near Bundaberg.
"The challenge now is that we've got multiple events going on."
QUEENSLAND'S 2013 FLOOD CRISIS
- The body of an elderly man was recovered from floodwaters earlier today
- North Bundaberg being evacuated after the Burnett River broke its banks on Sunday
- Up to 100 homes and businesses already flooded
- Fears up to 200 other properties could go under
- Disaster declaration now covers most low-lying suburbs of the city
- Burnett River is now expected to peak at 9 metres sometime on Sunday; the peak in 2010/11 floods was 7.5 metres
- Evacuation centres are taking in those forced to leave their homes
- Bundaberg region hit by six tornadoes since 1pm (AEST) on Saturday, Jan 26
- Tornado damage to homes and businesses in Burnett Heads, Bargara, Coonarr and Burrum Heads
- Rooftop rescues have been carried out in towns of Widgee and Sexton, west of Gympie, mayor says
- 27-year-old man is missing in floodwaters after trying to cross Widgee Creek, near Gympie; two others rescued
- Widespread flooding in the Gympie and South Burnett regions
- Mary River expected to peak at 17 metres, just shy of levels reached during the 2011 floods, on Sunday afternoon
- River expected to cut city in two
- Parts of Gympie CBD expected to flood
- Many major arterial roads cut, including the Bruce Highway
- Boyne Island and Tannum Sands, south of Gladstone, experiencing unprecedented flooding
- 900 homes evacuated
- Some homes flooded to their ceilings at Baffle Creek, between Gladstone and Bundaberg
- Water levels appear to be dropping, mayor says
- Concerns for 4000 low-lying properties in the region, north of Brisbane
- Evacuation centres opened on Bribie Island, and at Caboolture and Dakabin
- Huge swells causing severe beach erosion
- Reports of localised flooding
- Brisbane expecting six hours of cyclonic winds and torrential rain from about 2pm (AEST)
- Residents warned to prepare their properties with forecasters warning there could be more tornadoes
- Forecasters say the city will get 200mm to 300mm of rain over next 24 hours; some areas could get 400mm.
- Winds of 60 knot, or 125kph, equivalent to a strong category one cyclone, expected
- Some reports of localised flooding including in bayside suburbs
- Mayor urges residents worried about flooding to evacuate before it's too late
- Worst of the weather yet to hit the region
- Storm surges, 125kmh winds and torrential rain expected
- Evacuation centres set up at Nambour, Noosa and Caloundra
- Reports of localised flooding
-AAP
