We flew with our daughter at Christmas on AA (she was 6 months old at the time). She had her own purchased seat. We were never asked for any ID for her by the airline or at the TSA security checkpoints, although we did bring her birth certificate and passport just in case they asked for it. We were even able to check-in online to print her boarding pass without any problems. If CO is anything like AA with respect to infants in a seat, then it is not likely that you will need any ID. Bring her birth certificate just in case though.
Hope this helps!