Wow Cookerhiker, that's quite a trip. That's over 4,000 miles of driving !!! Without knowing your exact itinery, here are some suggestions for places to visit,
South Australia - Flinders Ranges NP, Coorong NP, Kangaroo Island
Victoria - Port Campbell Coast, then from Melbourne (& Phillip Island) drive up through Alpine National Park to Mt Kosciuszco (make sure you do the Lakes Circuit walk rather than walk straight up Mt Kosciuszco, about a 13mile day hike, but awesome). Then head back to the coast & follow the coast road north to Sydney. Many small towns & beautiful beaches & small national parks.
New South Wales - the Blue Mountains National Park just west of Sydney. Maker sure you have a few days to look around Sydney...it is a fantastic city (I am totally biased of course !)
National Parks are managed by each state so each of them has seperate web sites with info, but here is a site that will get you started
www.australiannationalparks.com. Just be aware that it does not list every park (even some of the most popular ones ????) so follow the links to the relevant states National Parks service for complete details.
There are a couple of spectacular short day hikes around Sydney Harbour. I would love to show you around if you have the time. Let me know if you have any time available in Sydney & I will send you my contact details.
Cheers,
Kaptain Kangaroo