I think you will find that issues relating to all children fall under the Family Law Act 1975 (Commonwealth). They are dealt with through the Family Court, the Federal Circuit Court (Federal Magistrates Court) or the Local Court. These courts cover issues relating to child custody laws, residence of children and ongoing financial support of children. It doesn't matter whether the parents are married, de facto, same sex couples or adoptive. The court will issue a Parenting Order based on what arrangements you wish to see in place, but taking into account as their top prioirty that which is in the best interests of the child. Children have a right to access to significant others, such as Grandparents, and these arrangements and rights will need to be sorted as well.
It seems things are done slightly in each state. You can either directly approach the Family Court in your state, or seek guidance &/or help from a family law firm if you have the money and want to minimise the stress and maximise your chances.
Good luck with it.
Blue