well i can help.

my daughter is in the same boat
but i didnt have her biological father on the birth certificate, so i added my husband to the birth certificate and changed her surname.
it is a few pieces of paper.

but you will need to get him sign away any rights to her and if you wish you can remove and amend the fathers name to be your new partner if you wish

and to change her name u need your signature and her fathers signature to say his approves and is happy to have her name changed

we filled out a change of name form
and an ammend birth certificate details/father name details form

cost about 250 all up but was worth it

now my DD has her "father" on her birthcertificate and the same name as me

she was 13 months old when we did all this.

they changed her name on the birthcertificate as she was so young and nothing was really in her original surname. centerlink and medicare just changed her name and took a copy of new certificate