If you are flying a U.S. company, this is allowed by the FAA.

Be aware though, that this is doing you a favor so approach it that way. Be really nice about it and make it clear, you're not expecting it but are grateful if they can do it.

They will not move any full fare passengers around to accommodate you. I did have someone complain that there were empty seats but they couldn't put one next to her. They will not shift everyone around to arrange this.

It's a win-win situation IF there are open seats. Less baggage for the handlers, more room for the baby, safer for baby and others around...