You will most likely have to drive it on the present rego as most states won't let you transfer the rego to your name unless you have a licence and address in that state or territory, and of course then the seller is taking a risk on getting fines in the mail for your tolls/red lights/speeding etc
Happened to me in Qld without the car I sold even leaving the state I got a toll bill because transport were slack to transfer info to toll roads.
And you will then most likely have to get a new safety certificate/rwc to reregister it in WA ??
Or you could get permits but they would have to be for all the states you are travelling in.
It's really simple, just click a box and print out a permission page and you can cross the border.
I also used a website called coseats.com and found someone who would drive me up for $60. At the last minute, he asked me if I could drive a second car and follow him up which I did and didn't have to pay anything for the trip up to qld as he paid for the fuel.
Then I drove my new baby home.
Stayed for a night in Gold Coast and basically back home in about 36 hours in total with car.