PFLAG stands for Parents, Families (and Friends) of Lesbians and Gays and is an international peer support group that has been operating in Australia for over 30 years. PFLAG Brisbane operates under the auspice of the Queensland AIDS Council. They have an extensive range of resources with information about sexuality and gender, most of which are targeted at parents.
PFLAG Victoria provides a limited range of resources, as well as having regular gatherings for parents, friends and families in Melbourne.
This site has a number of resources and links to other parent/family support networks.