A Commitment Ceremony or a Renewal of Vows is a great way to recognise and importantly, celebrate the love and commitment you share - without it being legally recognised.
The ceremony would include all the important components of a Marriage Ceremony (couples would say "I do, make vows to each and even sign a Commitment Certificate). The only exception would be that the ceremony would not be registered and is not legally recognised.
Couples have Commitment Ceremonies for many various reason. So want to recognise their commitment and love - without including "the government".
Others, may have decided to get legally married either here or outside of Australia and now what to celebrant with an intimate gathering of family and friends.
Here is a link to a sample commitment ceremony.