From their website, it looks like under two year olds don't pay if they don't have a seat?

For fare purposes, passengers are defined as follows

Adult - Age 12 - 64
Senior - Age 65 and older
Child - Ages 2-11
Infant in a seat - Younger than age 2, must be at least 2 days old to travel. Applies to domestic travel, must be booked at same time as accompanying adult(s).

Their website also says that you have 24 hours in which to cancel your booking if you booked online.

AA.com allows you to place certain reservations on hold. AA.com will reserve it for you for 24 hours (and some international flights up to 72 hours), unless advance purchase requirements prohibit this. In that event, your reservation will only be placed on hold until 11:00 p.m. of the same day the reservation is made.