I see a number of buses and other vehicles in Aus from overseas, England, Europe, the US and other countries according to the number plates, people doing a world trip. some of them are towing caravans. I would hopefully assume that they are here legally with correct paperwork.
NRMA (in NSW) used to provide an advice service for aussies to do the same thing. Possibly a Carnet de Passage to ensure that it comes back out and not an excuse to import and sell and any appropriate signage.
The only possible complications may be hooking up euro power to the CT you may need adaptors/rewire of connectors.
Personally I think it is doable, but is it worth it as opposed to buying/hiring one over there and selling/returning at the end of the trip?