Mmmhmm. Cool story, bro. As it happens, I don't think human babies have rights. All the protections they get from me flow from their adult guardians--which are likely coincident with their parents, but not necessarily.
The specific trait I am looking for is moral development sufficient to uphold the moral contract. I know a number of nonhuman species whose rights I respect on this basis, and I am nonhuman myself. Sapience is wisdom, not humanness.