Just a basic transformer AC-AC. Output 9Vac - 12Vac is fine. Not sure what’s inside any particular Halogen or LED transformer. Those online described as such don’t look promising. It should have waveform that is proportional to that of the line voltage.
Even if there is a suitable transformer with a AU plug, you will still need to calibrate to it and will only be guessing at the phase shift. My suggestion would be to get the UK or EU 240V transformer and spend your time looking for a socket or travel adapter to use it down-under.