Only Celebrants who are authorised by the Department of the Attorney-General of Australia are legally allowed to celebrate your wedding in Australia.
If your Celebrant is not authorised, your marriage is not legal. It's as simple as that. To check whether your Celebrant is a registered Marriage Celebrant consult the A-G's Register of Marriage Celebrants. This is a list of all Commonwealth-registered Marriage Celebrants who perform civil & religious ceremonies. It doesn't include ministers of religion or state officials who are also permitted to perform civil ceremonies. You can find more information about getting married and choosing your Celebrant here.