Simon,
Welcome to Perth !
No-where in Australia is it easier to rego a car than in SA mate.
Given that the car is currently rego'd there you should only need to have a roadworthy / engine number check type inspection when you hand the SA plates in and apply for WA plates.
I take it you have an engineers report from SA ?
First thing I would do is call Vehicle Safety Branch in Welshpool or your closest licencing centre and ask them what you need to do.
If you can't support the conversion with an eng. report then you may well need to engage a local engineer.
Brake tests only required if your system is not a complete one from a later model car, and an aftermarket ECU is no problem here.
PM me if you want to chat further.
(I went over the pits on Monday this week - passed no worries.)
Cheers,
Mitch.
(Classic Celica on Yahoo Groups)