From the carnival website------
Can I sail with my infant?
Infants must be at least four (4) months old to be eligible to travel, due to their vulnerable health. This is a company policy which takes into consideration the safety and comfort of the infant as well as the other guests. Carnival has fully researched the legality of the policy and it is not discriminatory and does not violate any applicable law. Carnival will not make exceptions and do not allow for the signing of waivers or releases to make an exception to the policy.
Fly-Aweigh infants (4 to 23 months of age) will be charged the "Cruise-Only" rate as long as the infant sits on a parent's lap on the airplane. If an airline seat is requested by the parent, then the infant will be charged the standard Fly-Aweigh rate. When an infant reaches 24 months of age, an airline ticket is required by the airlines.