Hi Kim,
The general rule is that if you want to take a child overseas you must obtain the permission of the other parent. For an Australian passport to be issued for a child, the law requires that each person who has parental responsibility for the child gives their written consent. If you are unable to obtain written consent of the other parent however, you can apply to the Senior Officer of the Department of Foreign Affairs and Trade for a waiver of the other parent's consent. I have heard that provided the other parent cannot provide good reason for withholding their permission, they will issue the passports.
Alternatively you can apply to the Court for an order permitting a child to travel internationally, which may be approved if the court determines it is in the best interests of the child.