It's pretty straight forward:
You don't stand a chance unless you are a permanent resident.
Should you opt for applying for permanent residency and eventually be granted one (good luck with that...), you would fall under the so called RPL (Recognition of Prior Learning) scheme, which is tailored for licenced ATCOs (including RAAFies).
Problem is though: You'll start at the bottom of the pay scale.
Conclusion: Not good enough.
Besides, ASA doesn't carry the best of reputations as an employer...
P.S. Kiwis have a special status since they have a right to live and work in Oz as such.