The only precautions one needs to take are the usual ones like insect repellents and the ubiquitous mosquito nets more so if you intend to visit the states of Northern Territory and Western Australia as a few cases related to mosquito borne ailments like Murray Valley Encephalitis and Ross River Virus have been reported there.
With regards to children all should have been subjected to the usual immunizations like tetanus-diphtheria, measles and chickenpox before travel to any foreign country. As one would take travel insurance to safeguard against any unforeseen calamity one would always be wise to be up to date on the health front as well.
As Australia is a developed country the health risks involved are at a minimum though it would always be better to see your family doctor or even a specialist in Travel Medicine to be on the safer side irrespective of where you are traveling. Some other related safeguards to be observed would be not going barefoot and bathing only in places that have been indicated as safe for bathers.