Hey I just did this exercise recently from SA. I was told by WA DPI to drive it back on the SA plates and re-register it in WA when the rego expired which turned out to be a load of rubbish.

Each of the states are like their own little independent flaming monarchy that rules its own kingdom

As soon as I notified SA that the car had been transferred because my drivers license is West Australian the car got deregistered (even in SA).

None of the ppl at DPI know how this works and as for the SA trans dept they are even worse!

I got back but was a bit of a drama getting this all sorted out.

Goodluck eh