I would also suggest bringing separate proof that you've booked the child a seat of their own, as you'll surrender the boarding pass when you board. We've had flight attendants question us (and not believe us) once on board about whether or not we'd purchased our DD a seat before she was 2 because the plane was fully booked and they needed all the seats. They asked us for her ticket/proof that we booked her a seat, and I just looked at her and said "they took all of our tickets when we boarded, but we bought her a seat."
Thankfully they verified it some other way, but it was frustrating at the time. I now carry an extra copy of her ticket (even though she's clearly over 2 now, it's just habit).
You may be interested in reading this "
Before you Fly, Know Your Rights" also.