Since 1901 (Federation) Australia has conducted elections and kept detailed electoral rolls. Included are some links to naturalisation records and some census records.
Queensland Archives has compiled indexes of their archival records. Use these links to get to the page and search the index database by name.
Once you get to the Queensland Archives page, here's how to use it:
You may also be able to download the full index using a link that will appear on the top right of the page or below the search box (depending on what device you are using, eg: desktop, iPad etc).
The Northern Territory Department of Arts and Museums is responsible for the Northern Territory Archives. A list of collections in the archive is available for download in PDF format (warning: 250+ pages) which can then be searched offline. The archives can also be searched online using the "Archives Navigator" service although it is not straight forward and no indexes are available.