CASA Regulation 2 para 7(a) has this covered. As soon as you advertise a flight in any way it is no longer a private flight and you are deemed to be operating commercially. For example, if you advertise in a public forum that you have a seat in your aircraft to go to a fly in, and you take someone who responds to your ad, you may be contravening this regulation even if you do not charge.
(7A) An aircraft that carries persons on a flight, otherwise than in accordance with a fixed schedule between terminals, is employed in a private operation if:
(a) public notice of the flight has not been given by any form of public advertisement or announcement