Hi,
This came from the Delta site, and since you mentioned you used Delta, this may help.
Infant Items
Last Updated: October 21, 2002, 3:00pm EDT
Children's Baggage Allowance
Below is the baggage allowance information you need to know when traveling with children.
Children traveling:
without charge do not have a baggage allowance.
for 10% of the adult fare (international travel) are allowed one checked bag plus one checked fully collapsible stroller or push-chair.
for 50% or more of the adult fare are entitled to the standard baggage allowance.
Checked Items
You may check child restraint seats and fully collapsible strollers. They do not count toward your allowance of two checked baggage items. Other infant items do count toward the two checked bag allowance.
Child restraint seats and strollers may be used to transport your child throughout the airport. Strollers must be checked at the gate by a Delta agent. Space permitting, you may use any adjacent unoccupied seat to secure the child restraint seat. However, if an empty seat is not available the seat must be checked at the gate by a Delta agent.
Carry-On Items
A fare-paying passenger may carry one bag plus one personal item on the plane. The following infant items may be brought in addition to the one bag carry-on allowance:
Booster Seats or other infant seats
Bassinets
Diaper Bags
Note: Only FAA Approved Child Restraint Devices may be used to secure an infant in a separate seat during take-off or landing. Otherwise, the infant must be held on an adult's lap at these times.
All carry-on items must fit easily in a Size Wise unit (approximate dimensions: 22"x14"x9") and must weigh less than 40 pounds.
Please remember that Delta cannot reserve a seat for a child restraint device unless a ticket has been purchased. However, if space is available after boarding is complete, you may use any adjacent unused seat to secure the child restraint device.
Each airline has different rules, if in doubt, go to the site and look under the baggage rules.