There is controversy within the law surrounding whether the religion of a newborn is determined by the religion of the woman whose egg conceived it, or the woman whose womb carried the child. However, in your case, since neither the egg nor the womb belonged to a Jewish woman, the child should convert. Since the baby is not considered to be of the age of reason, the conversion is done in accordance to the will of the parents, as long as she is raised in accordance to Jewish tradition. For your child to be recognized as Jewish by state institutions—the Ministry of the Interior and the Chief Rabbinate—you must do the conversion in a Minor Conversion Court. After the Minor Conversion Court’s decision, your daughter will need to go to the mikveh. The child can be immersed in the company of either parent. This is not a routine, monthly immersion, but a special immersion with a special blessing and must be done in special mikvaot, and during the day (not at night).
After this process, your daughter will be issued a teudat hamara (certificate awarded after conversion) and can have her status changed in the population registry to Jewish. When she grows up, she can marry any Jew other than a Cohen. When she registers, she will bring her teudat hamara. Beyond that, her conversion will not be registered on any other official documents.