The last time I looked into this, AA expected you to either pay for a seat and use a car seat or hold the baby for the whole flight! That's why, when I had a baby I always travelled with BA or QF.
Ignore the comments about traveling F with a baby - enjoy the flight but be aware that it won't be as relaxing as traveling on your own - but much nicer than flying at the back with a baby. Make sure you time the feeds so that you feed for takeoff and landing.