score:5
First off, while proof of onward travel is not a technical requirement for arrival in Australia, rocking up with (I presume?) a tourist visa that doesn't allow working and a one-way ticket is still going to raise some eyebrows at Immigration. I hope you have your story sorted out for this!
Russell already answered the car purchase bit, so I'll address the rest:
Actually renting housing in Australia is a massive, massive pain in the patootie that involves prolonged house hunts, handing over reams of documentation and hoping to win the application lottery; it's not worth it for stays of under six months, and as unemployed non-resident foreigners you'll be a few rungs below al-Qaeda members on the desirability index anyway. Your practical options are thus a) short-term rental sites like Airbnb and Stayz, or b) house sharing offers of varying levels of dodginess on Gumtree (the Oz version of Craigslist).
Upvote:4
There should be no problem in principle in buying a vehicle in Australia. I live in NZ and have bought and hired vehicles in Australia. The purchase was some years ago, but there should be no hard and fast barrier. Aspects like insurance may need care. Having documentary proof of a good insurance record in your country and your drivers licence will be required.
What aspects of buying a vehicle are you uncertain of in particular?
Prices are high compared to NZ. You'll need to check affordability before you travel.