From AA's site.
Infants are accepted two days after delivery, however, at least seven days is recommended.
Children under 5 years of age may not travel alone under any circumstances. Another passenger at least 16 years of age must accompany them. AA reserves the right to request documented proof of age for the adolescent accompanying a child under the age of 16.
Infants under 2 years of age who travel within the United States, Canada, Puerto Rico and the U.S. Virgin Islands may be held in an adult's lap at no charge. For transatlantic/transpacific travel or travel to/from Latin America, children under two years of age are required to have a ticket in their name for 10% of the applicable adult fare for the International portion. A 10% ticket does not entitle infants to their own seats. Contact Reservations for more details.
AA reserves the right to request documented proof of age for any traveler 2 years of age or younger. Please be prepared to provide documentation (birth certificate, passport, etc.) upon request.
For the safety of your child, American recommends purchasing a seat and using an approved child safety seat.
Children two years of age and older must travel in a purchased seat. See Seating Restrictions below for additional information.