The National Library of Australia offers some terrific resources for those researching their Australian family history.
One day (thinking I will need a week or more) I shall visit the library in Canberra but at present I use the eResources. I'd suggest that you take the time to browse the Genealogy Category so that you are aware of the resources available.
Most Australian researchers would agree that the best resource within the National Library of Australia website is Trove. It is an excellent source of information about our ancestors and times gone past (but you will need to wait until my "T" post to hear more).
An Australian resident can obtain a library card and then has access to a wider range of resources, such as 19th century UK newspapers.
Other "N" websites that I use for researching Australian Family History:
National Archives of Australia - this is covered more in my prior "Defense Records" post
news.google.com/newspapers - Historical newspapers from around the world. It is more difficult to find things than in Trove but it is interesting to browse.
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