You will find the main reason it's allowed over in the states is the fact that they have two geostationary satellites and a bunch of ground based, Wide-area Reference Stations (WRS) to ensure the integrity of the signal, whereas there is just the one over the pacific. (I'm unsure as to how many WRS's we have).
GPS approaches are available for many aerodromes in Australia, providing you're equipped with a TSO-149 certified GPS as this includes WAAS. These approaches often use ground based navigation aids such as a VOR or NDB, I'm unsure if it would any less legal if your GPS simply overlayed the approach on a map...