Maybe, maybe not.
My issues:
1) This kind of thing happens not infrequently. Yeah, it's bad but it's not unique.
2) If the infant was only one day old, did the mother deliver in a hospital? Did she know she was pregnant before she delivered?
3) While I want someone likely to be a serial killer either killed or locked away forever, I suspect this person is unlikely to do something like this again.
This may not be the silliest example of someone in prison, but I don't think the punishment fits the crime.