I fly with my children all the time. Unless you are flying out of the country, you don't have to provide any identification for the children. The rules on all domestic airlines are if the child is under 2, they can sit in your lap. If you buy a seat for a child under 2, you have to put him in a carseat. If a child is over 2 or turns 2 anytime during your trip, you have to buy a seat, but you don't have to put him in a carseat. I learned this the hard way after carrying 2 giant, heavy Britax carseats and two kids through the airports during my connections. So if you don't want to buy a seat, just don't say anything about his age; and if asked, lie. Because you don't have to provide any id for your child, neither of these airlines are going to expect you to be carrying his birth certificate and they will have to take your word for it. Happy traveling.