Australia is found within the Indo-Australian tectonic plate. Most seismic activity in the region occurs at the boundaries of this plate with adjoining plates. This is called inter-plate seismicity. However, a significant amount of earthquake activity occurs within the plate - both under the continent, and under the surrounding oceanic areas. This is called intra-plate activity, and the reasons for this kind of seismicity are not clearly understood. The map below shows seismicity for the 12 month period Oct 2003 - Sept 2004 ( from the IRIS website). This map shows clearly how most of the seismicity in the region occurs at the plate boundaries. The line of earthquakes to the south and west of Australia occurs along the mid-ocean ridges, which are centres of sea-floor spreading. Earthquakes to the east and north of Australia are at destructive plate boundaries, where subduction of the sea floor is occurring. Australia is moving to the north north east at approximately 10 cm per year, hence the many earthquakes at the collision zone with the plates to the north of Australia. 
The map below from the National Earthquake Information Center (part of the USGS) shows the distribution of earthquakes in the region over a 30 year period.  The map below, generated from the IRIS website, shows seismicity for the 12 month period July 2000 to July 2001. It shows in more detail how seismicity is associated with the mid-ocean spreading centres. 
------------------------------------------------------------------------------------------------------- Bathymetic map of the Australian region 
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