While I haven't yet had the need to research Australian genealogy records while building my family tree, I recently came across some free genealogy resources for there. I thought I'd pass them along in case one of my readers had Aussie ancestors.
The Australian Cemetery Index is a nice resource. It is searchable by surname. If you are not sure of how the surname is spelled, you can do a partial search on the surname. Unlike most searches which allow you to use a partial name, there is no minimum amount of letters you must use. You can search only the first letter of the surname. Information provided includes, when possible, name, date of birth, date of death, age, remarks, cemetery, portion and row. Some entries also include an image. The cemetery index does include some unmarked graves.
Find A Grave also holds a nice number of cemetery transcriptions and photographs for Australia. Be sure to check it for ancestors from other areas as well. The site predominantly covers United States cemeteries, but there is a growing number of ones from other countries as well.
The Australian Virtual Immigration Wall of Honor is a user-submitted database of immigrants to Australia. Information provided may include name, maiden name, birth year, birthplace, name of ship or airline, year of arrival, and port or airport of arrival. Since it is user-submitted, it is not a complete listing off all immigrants to Australia. However, as a free genealogy resource, it's worth checking.
AustraliaGenWeb is part of the WorldGenWeb Project. I'm a big fan of the GenWeb Project as it is free and can be helpful in tracing your family tree. The amount of data available on each project site can vary widely, but may include vital records, local history, military records, transcriptions for cemeteries or censuses, biographies and free lookups, just to name a few. Records are user-submitted so you will want to check back often to see what is new.
Cyndi's List has a massive listing of genealogy resources for Australia, many of which are free.