The answer is no. Riding a bike with ‘no hands’ is illegal Australia-wide. All states in Australia have the same laws that when cycling, cyclists must always keep a minimum of one hand on the handlebars at all times. If a police officer catches you doing so then you could receive a heavy fine.
You cannot have a part of your body projecting out of a vehicle says the Australian road rules. For example, waving out of the window or a sunroof you could receive a fine. However, don’t think that sticking your arm out of the window is illegal at all times, for example if you are parked and the engine is turned off you may do so.