My father was never named on the birth certificate, is he a guardian?

Being a guardian depends on the circumstances. Under the Care of Children Act 2004, the mother is a guardian, and the father is a guardian if he was married to the mother, or in a civil union or de facto relationship with her at some point between conception and birth, or if he is named on the birth certificate. A father who does not fit these categories is not automatically a guardian, but he can apply to the Family Court to be appointed as a guardian, and the court will consider the child's welfare and best interests, and the father's connection with the child. He can also apply for contact through a parenting order without being a guardian. Consider a formal agreement or mediation, so you both avoid unnecessary conflict.