My parents divorced, my father was my guardian, and my father took his children to travel to Australia. Do I need my mother's signature?

According to the general principles of civil law, parents of minors are guardians of minors. Even if the parents divorce, the guardian of the child is still the parents. Custody will not be released because of parents' divorce (except when the court deprives them of custody). In your divorce agreement, the father should be custody, not custody. Custody of both parents.

When a father takes his children to travel to Australia, usually the father can sign it, and the mother can do it without signing it.