Federal documents such as Birth Certificates and Death Certificates do not need to be notarised before they are apostilled. Other government documents that do not need a notary are:
Certificate of Residency issued by the ATO if the documents have a government stamp
Divorce Order printed in colour
Police Certificate from the AFP or State Police
Marriage certificate in the standard portrait orientation. Please not Marriage Certificates in the ceremonial landscape orientation will need to be notarised before it can be apostilled.

Generally if the government document has an official signature or seal it does not need to be notarised.

Many other documents issued by Government departments must be notarised before they can be apostilled.
Documents needing to be notarised include:
Article of Association of a Company
Australian Educational Documents
Letters of Employment

This list will grow as more examples are discovered.