Answer:
#1 , CALL THE AIRLINE ASAP about adding your baby to the intinerary
AGAIN............ CALL THE AIRLINE ASAP.
#2 Do NOT check the car seat as luggage. Check the car seat at the gate planeside. (tons of car seats lose those tags, label on the seat somewhere your contact info. also, baggage car seats tend to get banged up real bad, and if they get lost you won't have a car seat at the end of your destination) ** Car seats checked at the plane do not count as carry-on. Same goes for an UMBRELLA stroller (not the big strollers), and a diaper bag. **
#3 Bring the card AND his birth certificate (they need proof he is not 2. and they will not go by his looks. Birth certificate is needed for getting though TSA and the airline.)
http://www.aa.com/i18n/travelInformation/specialAssistance/childrenTraveling.jsp
Here is the company website for what you need for baby.
(I carry my lil one through the airport in a ring sling )
Also, all formula must be in original packaging, Water can be picked up past security, If you breast feed, that is so much easier! And bring double the diapers, bring wipes, and one extra outfit for him in your diaper bag to bring in the plane. If you meet all carry-on limits, you won't have to 'check bags' when checking in. Carry-ons can go to the plane, they do have $$$ carts to rent to help you carry if you have alot of stuff.
EDIT ---- TIM and NEIL are CORRECT. I HAVE FLOWN MANY MANY TIMES WITH BABY. Do NOT check the car seat as baggage, you might never see it again, GATE CHECK THIS PLANE SIDE. Does NOT cost anything. And bring that birth certificate. I fly Delta, Southwest and AA. And in a rare pinch I go on AirTran. If any other people read the link --- the stroller, car seat, and diaper bag can be taken to the plane gate. The SMALL umbrella stroller and car seat go on the cart plane side, diaper bag goes with you. None of these count as a 'carry-on' towards your limit.