With crowded airports and little space in airplanes, slings and carriers help carry your baby. Your hands stay free and babies feel very safe and generally enjoy being so close to you.
Child-restraint devices are optional; you are not required to secure your child in a car seat on the plane.
If you opt for taking a stroller, you will have to check it at the gate and reclaim it at your destination. However, check with your airline for their specific allowances.
If you are breastfeeding your baby, bring a nursing cover.
If your baby takes a bottle, make sure to bring enough formula for the number of feedings expected while in the air and at the airport. Bring more as your baby's eating habits might change while in transit. Also consider possible delays. If baby gets really unhappy on the plane, there is nothing wrong with treating him to an extra feeding.
If your baby eats solids, bring her food as well as a couple of plastic spoons.
There is no limit on bringing baby formula/milk in containers on board with you on most airlines. But check with your carrier beforehand to be sure.
In addition to formula bring liquids the baby likes, e.g., tea or juice. The Transportation Security Administration states that "baby formula and food (...), and juice are allowed in reasonable quantities exceeding three ounces and are not required to be in the zip-top bag. Declare these items for inspection at the checkpoint."
On the plane you can get hot water and juices, but it is better to have some with you in case the flight attendant is occupied or everyone needs to stay in their seats.
Bring plenty of diapers and wipes. Traveling can affect a baby's system and cause more frequent bowel movements, so it is better to be prepared and have extras. Don't forget to factor possible delays into transit time.
Airline toilets are equipped with fold-down changing tables. For sanitary reasons you should use a changing pad. Most diaper bags come with one; disposable pads are especially practical and do not take up a lot of space. If you run out of them, you can also use paper towels from the bathroom.
Your baby might not need an outfit change, but it is always better to be prepared. Bring at least two clean outfits with you and possibly a pair of pajamas if traveling on an overnight flight.
The air-conditioning system can cool down a plane, especially when flying overnight. Pack a blanket in case the airline does not have one available for you to use.
Plastic bags (scented) are essential for dirty diapers. They also come in handy to pack soiled or wet clothes, as well as leftover snack items.
For take-off and landing a baby should either be drinking or sucking on a pacifier to alleviate pain from popping ears.
New toys help to distract the baby when she is getting impatient on the plane.
If your child needs to take medication, make sure to bring it on the plane. Even if you do not need to give it to your child while in-flight, you want to have it in case your checked luggage gets lost. It is also smart to keep medication with you in case you need a pain or fever reliever for the little traveler.