You dont get the GST back when you reexport the aircraft if it was paid when the aircraft was originally imported. There are however at least 3 options:
If you are only going to be here a short time then you can temporarily import it. You have to lodge some guarantee with the ATO and then get that back when you leave. Usually the goods can be in Australia no longer that 12 months.
You can set up a business to import the Aircraft. You can then pay the GST and then claim it back as the cost of the Aircraft is a business expense. Is ever the business sells the aircraft GST will be payable then. Also the ATO take a dim view of having personal assets/activities set up as businesses and so expect some extra scrutiny if you go down this path.
You can pay the GST. But get good advice as the customs value can be a lot less than what you think that it is worth. For things like aircraft and boats there is a big difference between what the thing might sell for at a no reserve auction after 30 days of advertising vs what an owner might hold out for over a long period of advertising/negotiation. If you bought the aircraft a while ago then the value may be able to be justified as a lot lower than you expect.