Some airline web sites require that the person whose name is on the credit card be one of the ticketed passengers. Assuming your 2-year old doesn't (yet) have a card, you might need to go 2 and 1.

Also, to be sure that there's no glitch with the baby's ticket, you might want to go that way anyway. By my calculations, 1,000 miles isn't worth the torture of convincing AA that they shouldn't separate you and the baby by 25 rows...