In Australia you can only be married by a Commonwealth Registered Marriage Celebrant or a registered religious Celebrant.
You can marry if:
You are both over 18 years of age (if one of you is between 16 and 18 then you must have permission from parents or a judge)
You both understand and consent to marriage
You are not a direct relation of each other (You can’t marry your parent or grandparent or your brother or sister)
You are not already married.
As of 9th Dec 2017, there is no gender or sex preference bias in the Australian Marriage Act. Only a registered religious celebrant has the right to refuse same sex couples. I am a Commonwealth registered Marriage Celebrant and it is my privilege to marry you whatever your gender.
You must give at least one month’s notice of your intention to marry. Your Celebrant will have the proper forms for this.
If you are drunk or drug affected at the time of the ceremony, your Celebrant is legally obligated to refuse to marry you.