Since the child is in Australia, it would currently by governed by Australian law, but under Australian law, there is no statutory rule about who the child lives with following separation - the Family Law Act 1975 tells the Court what it can and can't do; it doesn't tell the parents what they can and can't do, and the Act only has force if one of the parents asks the Court to intervene due to an inability to reach an agreement between themselves.
So, how does this affect you? Basically, the child can stay or go depending on what the parents decide for themselves.
If you can't reach agreement, though, you can file an initiating application with the Court seeking parenting orders. The Court will make a decision based on what it is satisfied is in the best interests of the child.
Before you can file for parenting orders though, it is necessary that you and the other parent attempt to negotiate an agreement between you first by attending a family dispute resolution conference. I believe Legal Aid can provide some guidance on this, so it would be worthwhile giving them a call.