I assume that you are referring to the Search Bar, which is to the right of the Location Bar where URL's appear. You have the en-GB version of Firefox installed, which comes with the Google GB search engine. Install a Google - Australia search engine from here.
http://mycroft.mozdev.org/google-search-plugins.html

There are two listed, so make sure you install the one for Pages From Australia.

There are other things that need attention:

Your above posted system details show outdated plugin(s) with known security and stability risks that you should update.

• Java Plug-in 1.6.0_03 for Netscape Navigator (DLL Helper)

Update the Java plugin to the latest version.

• http://www.oracle.com/technetwork/java/javase/downloads/index.html (Java Platform: Download JRE)

Thought this might help some people.. I too had this issue and resolved it by the following. Open your add-ons manager in firefox, and under 'Extentions' you will likely have 'InstantFox' which is the add-on for searching via the address bar (not the search bar like assumed in the previous posts). Click on 'options', then on the advanced tab you'll have a 'Standard search withour shortcuts' area. Simply change the url from '.co.uk' to '.com.au', click ok, and you're all done. Hope it helps..