Who can marry in Australia ?

To get married in Australia, you must:

not be married
not be marrying a parent, grandparent, child, grandchild, brother or sister
be at least 18 years old, unless a court has approved a marriage where 1 person is 16-18 years old
understand what marriage means and freely agree to marry
use specific words during the ceremony
give a notice of intended marriage form to an authorised marriage celebrant at least 1 month and no more than 18 months before your wedding
be married by an authorised marriage celebrant

You don't have to be:

an Australian citizen
a permanent resident of Australia

If you are not an Australian citizen or permanent resident of Australia and you want to live in Australia after your marriage, you should find out about getting a visa

Marriage equality

The right to marry in Australia is no longer determined by sex or gender.

https://www.ag.gov.au/families-and-marriage/marriage/get-married