I work in with licensing services for DPI so i know all this.
Transfer papers DO NOT need to be filled in. When you pruchase the car, all you need is a receipt of payment made for the car showing that you are the new owner. Once the vehicle gets into WA you need a tempory movement permit to take it to the pits, have the inspection done and pay for WA rego and plates.
The fees involved are as follows:
Temporary Movement Permit - $13.85 (pay over phone by credit card or go to Licensing Centre. Same for all transactions)
Inspection @ Pits - $83.30 for first inspection, $58.10 if you need to go back.
Rego on an R33 - between $240-$260 for 6months, $420-$440 for 12months. Can't give you an exact fee on that one but the fee wont change by much.
WA State Plates - $13.00
What to take with you to the pits:
The vehicle (obviously), your id (WA Driver's Licence card) and a eftpos or credit card or something, receipt of purchase for the vehicle, and yourself Also make sure the vehicle has an immobiliser as this is law in WA.
I can't really help with regards to having it pass the pits and mods etc, sorry.
There's the full process
Just PM me if you need anything more.
Cheers,
Jason.