I have done Australia in a PA32 but the 172 is a bit of a challenge.
The road network is probably the best bet.
How about this trip Fantome.
The Outback Way: Perth to Cairns
The Outback Way is the granddaddy of shortcuts, Australia's longest. Stretching an epic 4615 kilometres from Perth to Cairns via Uluru and Alice Springs on a network of well-maintained dirt roads such as the Great Central Road and the Plenty Highway, it's not exactly short but it certainly cuts – about 1000 kilometres compared with driving Highway 1 and other main roads. See outbackway.org.au.
Read more:
Road trips around Australia: The 12 best Aussie shortcuts for driving
Follow us: @TravellerAU on Twitter | TravellerAU on Facebook