His rights is set out in the Children's Act, sections 18 and 21:
18. Parental responsibilities and rights.—(1) A person may have either full or specific parental responsibilities and rights in respect of a child.
(2) The parental responsibilities and rights that a person may have in respect of a child, include the responsibility and the right—
(a)to care for the child;
(b)to maintain contact with the child;
(c)to act as guardian of the child; and
(d)to contribute to the maintenance of the child.
(3) Subject to subsections (4) and (5), a parent or other person who acts as guardian of a child must—
(a)administer and safeguard the child’s property and property interests;
(b)assist or represent the child in administrative, contractual and other legal matters; or
(c)give or refuse any consent required by law in respect of the child, including—
(i)consent to the child’s marriage;
(ii)consent to the child’s adoption;
(iii)consent to the child’s departure or removal from the Republic;
(iv)consent to the child’s application for a passport; and
(v)consent to the alienation or encumbrance of any immovable property of the child.
(4) Whenever more than one person has guardianship of a child, each one of them is competent, subject to subsection (5), any other law or any order of a competent court to the contrary, to exercise independently and without the consent of the other any right or responsibility arising from such guardianship.
(5) Unless a competent court orders otherwise, the consent of all the persons that have guardianship of a child is necessary in respect of matters set out in subsection (3) (c).
21. Parental responsibilities and rights of unmarried fathers.—(1) The biological father of a child who does not have parental responsibilities and rights in respect of the child in terms of section 20, acquires full parental responsibilities and rights in respect of the child—
(a)if at the time of the child’s birth he is living with the mother in a permanent life-partnership; or
(b)if he, regardless of whether he has lived or is living with the mother—
(i)consents to be identified or successfully applies in terms of section 26 to be identified as the child’s father or pays damages in terms of customary law;
(ii)contributes or has attempted in good faith to contribute to the child’s upbringing for a reasonable period; and
(iii)contributes or has attempted in good faith to contribute towards expenses in connection with the maintenance of the child for a reasonable period.
(2) This section does not affect the duty of a father to contribute towards the maintenance of the child.
(3) (a) If there is a dispute between the biological father referred to in subsection (1) and the biological mother of a child with regard to the fulfillment by that father of the conditions set out in subsection (1) (a) or (b), the matter must be referred for mediation to a family advocate, social worker, social service professional or other suitably qualified person.
(b) Any party to the mediation may have the outcome of the mediation reviewed by a court.
(4) This section applies regardless of whether the child was born before or after the commencement of this Act.
It follows that he can only enforce these rights as soon as the child is born.
I must also add that his chances of getting custody over a new born is almost non-existent. For him to get it, he would have to allege and prove that the mother is a drunk, a prostitute or a drug addict, none of which applies to your daughter, I am sure.
I would suggest that, as soon as the child is born, or even before if she is up for it, that your daughter and the father attend the Family Advocate in order to get a parental plan negotiated and registered.