Be sure to bring proof of child's age with you when you check in at the airport.
Consider how you will get to your boarding gate when you have to take a baby, car seat, stroller, diaper bag, and your carry on bag through the airport
If you plan to travel by car at your destination, you'll need baby's car seat. Rental cars typically have child seats for rent, but you never know the size, style, availability and quality. Better safe than sorry.
Most airlines let children under age 2 ride in an adult's lap. You can check your child's car seat with your other luggage, and wrap the seat in plastic or a bag for protection. Some suggest buying baby a child's ticket and using the car seat on the airplane, no matter the age. Babies can be injured while flying, when a parent can't hold on during severe turbulence. If your flight isn't full, you may be able to take the car seat on board and use it without buying a ticket, if seats are available.
One carry-on bag needs to serve as purse, briefcase and diaper bag, and a most suitable option is a large backpack, which is easy to carry when your arms are busy carrying or controlling your child.
Strollers are handy when babies get heavy or toddlers are no longer able to walk or keep up. Many infant car seats snap onto a travel system stroller, so you can take both along for the trip. Otherwise, a lightweight stroller with a carrying strap is easy to haul around, and can help make that connecting flight with your toddler along.
At your departure gate, ask the gate agent for a "gate check ticket" for your baby's stroller. Gate checking means you leave the stroller at the gate or jetway just before boarding the airplane, and it will be waiting for you as you exit the plane after the flight. This is most convenient if you need the stroller for a connecting flight. Airlines typically allow parents traveling with babies and toddlers to board the plane early, giving you more time to install a car seat and get settled.
If you purchased a ticket for your baby, keep in mind that baby car seats can generally only be installed in a window seat on most airlines, which impacts your seating assignment. Check the baby seat's manual to be sure that it is FAA approved for air travel. Airline seatbelts can be hard to tighten when buckled with a car seat, so you may need flight attendant assistance.
A baby sling or backpack carrier may be handy for carrying baby quickly through an airport, too. This helps to keep a baby close when the baby doesn't have a ticketed seat, but generally may not be used during takeoff and landing, so need to be stowed at such times.
If you're preparing for a long trip, add a set of travel straps to baby's regular car seat and wear it like a backpack. Look for disposable feeding supplies like bibs, bottles, sippy cups and utensils to speed/skip clean up during your trip. And bring along a few new toys to keep baby entertained!