Later on it is understood they survived by putting out plastic containers to capture rainwater, and rationing their food.
Steven Van Lonkhuyzen, 37, Ethan, seven, and Timothy, five, are thought to have become stranded without a mobile phone signal when their four-wheel drive vehicle got bogged down in mud caused by heavy rains.
The family disappeared on a 1,000-mile road trip from their home in Brisbane, Queensland, to Cairns in the north of the state.
A farmer found them at the Expedition National Park near Taroom, 400 miles north-west of Brisbane.
Police spokesman Mick Bianchi said: “We have police and park rangers heading up there to figure out the best way to bring them out.”