Hello Jason
You have made a good decision to go to Cairns in September. From November until March the humidity is uncomfortable.
The Red Centre, as a guess is around 4000 km by road from Cairns. Best done through an organised tour out of a State capital. There is so much isolated Central Australia scenery that needs an expert to find quickly. To drive to Brisbane is an overnight stop but on way are nice Great Barrier Reef towns on coast (off highway). If you just drive you are on an ugly highway and you will miss the good areas.
Cairns and to north has many nice attractions, Below is a URL which will lead to many links of attractions. There are good wild life zoos, Crocodile attactions, Rain forests, Great Barrier Reef tours, Aboriginal arts and so on.
I go to Cairns in December and Flickr has a few photos. UV is bad then. Suggest all family get used to strong sun and sunburn.
For camera, a high quality CP will be necessary for strong sunlight
Link to Cairns is
http://www.cairns.aust.com/
http://www.cairns.aust.com/listingView.html?listingId=415
http://www.cairns.aust.com/location/Cairns/listingView.html?listingId=1022
Flickr link to my last Cairns visit is
http://www.flickr.com/photos/shebalso/sets/72157611384481502/
A must is a day trip to
1. Port Douglas morning and afternoon Cairns Botanical Gardens ( may be boring for children though )
2. Cape Tribulation by organised tour. No use driving yourself as you will miss the best scenery
3. Karauna Rail tour,return by sky rail
Later I will include links to out back but nothing is close out side capital cities. Australia is near size of USA and 21 million.
Drive yourself will save time in waiting for tours to start but getting lost is easy and you miss the expert commentery
Regards
John