Click on a station name in one of the drop boxes. You will then be taken directly to the statistical data for the site chosen, on the Bureau of Meteorology's rainfall data site. The stations are listed in alphabetical order to make searching easier.
When viewing the monthly data, if you click on a year at the left hand side of the table, the daily data for that year will be displayed.
You can see the data for all Australian stations, including ones that are now closed, by clicking on this link.
Please refer to the copyright notice before using this data.