Guardianship of the child will be the determining factor in this situation. What it boils down is that you will have to show an insurable interest in the child, typically meaning you are the parent, guardian, or caregiver. If your domestic partner is your dependent, then the child would naturally be your dependent as well. If your domestic partner does not rely on your for support, has her own insurance, or if domestic partnerships are not recognized, then you would not be allowed to add a life insurance rider for the child.
If the state you live in recognizes domestic partnerships but your insurance company does not, or if your insurer recognizes then and the state does not, you can still add the child of your partner. If the state recognizes domestic partnerships, the insurance company must honor the law, but if the law does not recognize them, the insurance company still has the option of treating your partner as though she were a spouse.
If you are not able to add the child to your life insurance, your partner will be able to. As the birth mother and primary caregiver for the child, your partner cannot be denied the ability to insure her child. However, it might be a better idea to get life insurance quotes for a standalone policy for the child. That will guarantee insurability even if medical conditions develop later in life, and give the child the lowest rates available on the premiums.
Either through your own policy or that of your domestic partner, the child will be insurable when it is born. If you are legally recognized as domestic partners, then you have the rights of a spouse where the child is concerned, including the ability to buy or change insurance policies for life and health coverage. Bear in mind that adding a child rider will increase the cost of your premiums somewhat, but not a great deal.