To update your legal name and gender on your existing drivers license, you will need to fill out two forms, the DL2 for changing your name and photo, and the DL25 statutory declaration of gender change.
The cost is around is $50
The latter needs to be signed by you in front of a Justice of the Peace, Lawyer, Medical professional, or other person authorised to witness a statutory declaration. A Justice of the Peace is free, and a list of your local JPs can be found here.
This can then be taken to a licensing agency, who will take your photograph and send your application away to be reviewed.
Your new licence will arrive in the post.