Had pretty much the same problem with my daily, I had to apply for new registration via a form TransportSA gave me, then I had to get the car ID inspected at Regency even though it had SA plates and everything...
I should note that when I did this I didnt have to show them proof of purchase or anything, I had absolutely no paperwork worth anything there...
edit: I also registered a car from Victoria with no paperwork too, although I did a have a reciept for the car