See this from their website under "Travel Info"; I have bolded the answer to your questions.
Children and Infants
AirTran Airways strongly encourages customers traveling with infants less than 7 days old to consult with their physician prior to traveling. One (1) infant under two (2) years of age, not occupying a seat, may be carried free of charge in the lap of a customer paying the applicable adult fare (AirTran may request a birth certificate to validate the infant's age).
You may bring a stroller to the gate for ease of travel through the airport. The stroller may be gate checked just before boarding the plane and will be returned to the aircraft jet way upon arrival at your destination. Car seats and strollers may be checked free of charge; any other items are subject to standard baggage fees (i.e., portable crib, high chair, etc.).
Booster-type child seats, vest and harness-type systems, and lap held child belts are not approved for use in the aircraft during movement on the surface, taxi, takeoff and landing; they may be used during cruise flight only. The C.A.R.E.S. (Child Aviation Restraint System) is currently the only child safety device FAA approved for all points of travel, in place of a child restraint seat.
When traveling with an infant, you are allowed more than the standard one carry-on item in order to travel with baby-related items such as diapers, baby clothes, blanket, etc. We recommend that you carry on an ample supply of baby care items in the event that your flight is delayed. Security requirements prevent us from retrieving checked luggage from the cargo stowage.