If you do a weblookup on "buying a vehicle in Australia" and include the State that you are arriving in. You will get the official "transport departments" viewpoint/checklists.
NSW is the hardest State to own a vehicle as it needs to have an annual vehicle roadworthy inspection, I think all of the other States only require one prior to selling.
Australia is a Federation of States - just like the USA or EU, and the laws that apply are slightly different in each State - or they use different terminology (eg RWC (roadworthy certificate), Safety Certificate, Blue Slip - all essentially the same thing).
Selling the vehicle in another State is hard if you find it hard to cope with bumbling bureaucrats, I'd accept $500 less and sell unregistered.
Prior to registering the vehicle in your name you will need to prove who you are - passport, drivers licence, credit cards, etc. PLUS something with a local address (rent receipt) which many Hubbers are happy to help out with given plenty of notice.
All of the motoring clubs offer pre purchase inspections which go well beyond the legal minimums, depends on how much you paying, often come with gurantees.
Insurance causes the biggest confusion - as part of the annual registration fee you must pay for third party injury insurance. You must buy additional insurance to cover damage that you may cause to others' property (third party property) or to cover damage to your own vehicle and others (comprehensive).
Third party injury insurance covers you in the event of an accident EXCEPT in some States if you are deemed at fault then you will be presented with a bill one day.
Drugs and alcohol immediately void your insurance.
Zero % illicit drugs whilst driving, 0.05% blood alcohol. Prescription drugs as per your doctors orders about driving.