What are child custody rules in Australia?

I'm about to give birth & my partner has left. I am happy for him to have access to our daughter when she is born & have want to set up an agreement to avoid any conflict. However, I can see him making things as difficult as he can & want to know how to get full custody so that he can't ever threaten me with that. Also I've read answers to this same question from people in the USA & they say stuff like don't put his name on birth certificate until you have full custody. What happens in australia? She is going to have his last name but does he need to sign anything agreeing his father? Can he take her if I name him as father? Can that be added later? HELP!!