Assuming that zygotes are not moral agents and healthy, intelligent, rational, human adults are moral agents, at what point(s) do(es) their status change? What arguments have been offered for those points' significance? Are there intermediate stages of moral agency?
That point of conversion from amoral agent to moral agent is not clearly defined, and may be intrinsically vague. You might start by asking, "does moral agency have clear existential borders, or can it exist as a matter of degree?"
It's been pointed out before that we should not seek to do philosophy here on Philosophy.SE, so rather than engage in a conversation on the topic I'll just refer you to the sources on the subject.
Jean Piaget is probably the best person to start with on the subject of childhood development and morality. If you can dig up any of his papers, many of them begin with this very topic.
For a general review of childhood as a philosophical status, try the Stanford Encyclopedia of Philosophy.