Under NSW legislation the birth mother is always recognised as the sole legal parent if she is not in a marriage or a de facto relationship at the time of the conception. Persons who have not donated their eggs or sperm are not recognised as the legal parent.
The situation is not so certain and definitive under the Commonwealth legislation of the Family Law Act. Judges have taken differing approaches and your case needs to be reviewed carefully.
You may wish for certainty so that you and your partner are both to be recognised as having parental responsibility in the long term decision making processes for your child in such matters as location for living for you and your child, education, health and religious upbringing.
Speak to Fay about taking proceedings in the Family Court in a non-confrontational situation before problems arise. Even if you and your partner have separated you wish to may seek orders from a court to determine who will have the parental responsibility for your child.