Bring the baby's birth certificate! Just in case.
If you are not checking your stroller - always fold it down yourself. This will prevent the chances of it being broken when you get off the plane!
It is free to check a car seat and free to check a stroller. Take them with you to the gate and they will tag it for you or check them with your luggage.
Try to show up at your gate a little early. Sometimes a sympathetic employee can shuffle seats around so you can have a little extra room to yourself and even use the car seat.
If you have a baby you can bring breast milk or formula through security. You will have to take it out and show it to the security workers.
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