Some, like Queensland’s QGIS (not to be confused with Quantum GIS), offer users the ability to download data for use in software like Quantum GIS.
Other state departments have geospatial data available here:
VIC <http://services.land.vic.gov.au/SpatialDatamart/index.jsp> and <http://www.vic.gov.au/about-victoria-tourism/maps/geospatial-data-maps.html>
At a national level, Geoscience Australia has developed a tool called MapConnect that lets the user download local spatial data fur use in QGIS and other GIS software packages. There is a very good help function available with the tool.
Public health data for Australia and the states <http://www.publichealth.gov.au/interactive-mapping/social-health-atlas-of-australia%3a-statistical-local-area-and-local-government-area_-published-2012.html>
Internationally, there are many agencies providing useful data online such as:
The following library collections hold useful global resources that can be downloaded and used with various software packages.