For the wedding ceremony to be legal under the requirements of the Marriage Act 1961 (Commonwealth) the ceremony must:
Have the celebrant introduce themselves as an authorised celebrant.
Have the couple’s full names said (either by the celebrant or the couple themselves) out loud during the ceremony (before or during the vows).
Include the reading of the Monitum by the authorised celebrant:
I am duly authorised by law to solemnize marriages according to law. Before you are joined in marriage in my presence and in the presence of these witnesses, I am to remind you of the solemn and binding nature of the relationship into which you are now about to enter. Marriage, according to the law in Australia, is the union of a man and a woman to the exclusion of all others, voluntarily entered into for life.
Include an exchange of vows as recognised by the Marriage Act 1961 (Commonwealth) that declares each party to “lawfully wedded” to each other and that each “takes the other” to be their husband/wife.