daviojk,
There is no limit to how long a non-VH- aircraft can be flown in Australia, on private operation. You have to comply with GST rules, but that is nothing to do with CASA. And that does NOT automatically mean you have to pay GST on an import, you need expert advice on that one.
Nobody in their right mind would register an aircraft in Australia, if they had a practical alternative.
NZ or N- probably the best for a small GA aircraft, lots of choices if you have something bigger, Bermuda, Aruba, Isle of Mann are several that come to mind. Do not even think about several West African countries that offer such services.
Just about all of them require a "nominal" residence of some legal form in the country of registry, but it is seldom a barrier, just an expense.
Tootle pip!!