Does the Catholic Church regularly excommunicate people who kill children(ie the ones that have been born)?

While I think that the people excommunicated will be far better off without the church, I think it will take them a while to realise it. In the meantime though, these actions will just traumatize the poor girl further than she already has been. It really seems to me that they are just using this girl as an example to show that there are no circumstances where they will tolerate abortion. Pretty despicable if you ask me. Hasn't she suffered enough?