Yes you can, but there are several hoops to jump through, Jaba covered most of them nicely, but there's a couple gotchas, see below.
That was me, and eventually I gave up and went back to RAAus because I didn't have my MPC at the time and wasn't prepared to pay for a LAME to issue a MR, or a WCO to redo the W&B per the AP's requirement, even though it had been done by an RAAus L4, an approved CAsA delegate. The difficulty of getting in touch with either of the (at the time, only) two AP's in NSW didn't help either.
Now I have the MPC, when I can tee up a time I'll have another crack, but here's a few tips:
Make sure you de-register your aircraft with RAAus well before you attempt to register it with CAsA.
Where the CAsA registration form asks "Has the aircraft ever been on a foreign register?", the muppets in Cant-berra interpret this to mean "Any register other than ours, at any time since Noah built the ark?", not just "A register in another country"
You can register your plane VH at any time, but you can't fly it until you have a CoA from an AP
Unless you built it, or "a substantially similar" one, you will need a LAME to raise the MR, which can't happen will you have a CoA
The AP or LAME may want a new W&B done. If you haven't done the MPC & W&B course, you will need a CAsA-approved WCO to do this. Ask beforehand.
The AP may want to issue you a test area to complete your "SAAA-approved" Phase-I testing, even though you have successfully been flying RAAus for months/years. Ask beforehand, and discuss where this area will be.
The AP may want you to complete the SAAA "Risk-Radar" bollocks, even though you have successfully been flying RAAus for months/years. Ask beforehand and discuss.