National Health & Medical Research Council NH&MRC
Grant Application and information, forms and instructions
http://www.health.gov.au/nhmrc/

GrantsLINK
http://www.grantslink.gov.au

Australian Academy of Science
http://www.science.org.au

Awards and Grants for Research Conferences
http://www.science.org.au/awards/awards.htm
The Australian Academy of Science makes several awards for excellence in science. These awards cover disciplines in the physical, biological, earth and mathematical sciences and the application of science to industry, including exploration for minerals. The awards may be marked by the receipt of a medal, the delivery of a lecture or the provision of funding for travelling fellowships or scholarships.

Scientific Exchanges, Fellowships and Grants
http://www.science.org.au/internat/exchange/contscix.htm

Australian Research Council
Grants through the University of Melbourne
http://www.research.unimelb.edu.au/arc/

Victoria: VicHealth research grants
http://www.vichealth.vic.gov.au/funding/
(They have a program in mental health research)