There is no one set direction in which water would rotate as it goes down the drain in Australia or anywhere else in the world.  Many people believe that water in the Northern Hemisphere rotates in one direction and water in the Southern Hemisphere rotates the other direction.  This is not true.

The logic that is given in such arguments centers around something called the Coriolis Effect.  Because of the Earth’s rotation, masses of air move in different directions in the Northern and Southern Hemispheres.  In the Northern Hemisphere, the winds in hurricanes flow counter-clockwise while in the Southern Hemisphere they flow clockwise around the center of the storm.  The Coriolis Effect also has an impact on the direction in which ocean currents flow.

However, the Coriolis Effect is much too weak to have a significant effect on something as small-scale as the flow of water in a bathtub.  It does have some impact, but that impact is so small that it is easily overwhelmed by other forces.  Therefore, the direction in which the water flows as it goes down the drain is determined by other forces such as the shape of the tub, the currents that are already at work in it (from a person being in the tub, and the shape of the drain.