And to generate income and hopefully make profits and pay tax with the aircraft, you need an AOC. No AOC and either CASA or the ATO may take a lot of interest in your activities.
Our last "private" aircraft was purchased through a company registered for GST, so we claimed the GST back. We put the aircraft on-line with the local aero club with a written contract.
We had an ATO audit and they were happy with the contract arrangement. No AOC required.