Well, we traveled with our daughter who was right around that same age last year. I packed a bag of small, quiet, toys that were new and she had not seen them before. As soon as she got tired of one, I pulled out another. I also took a dvd player and movies. And of course, her favorite snacks. We decided to gate-check her carseat since we did not purchase a seat and have her sit on my lap in a harness I ordered from One Step Ahead. I have heard that if the flight is not full they will allow you to use your carseat even if you did not purchase the extra seat.
Other well-traveled moms recommended gate-checking the carseat because it does not end up with as much damage. However, it was difficult to maneuver a large carseat (got a case for it with wheels), stroller, etc through the terminal even with my husband's help. I did see one at the airport where the carseat doubles as a stroller with some attachment that makes it look like you are pulling luggage, but I do not know where you find it.
I also took our monkey leash, it's a backpack that looks like a monkey and it's tail is the part I hold. This worked well for when she wanted to walk. I got ours at Target, but I have seen them at Wal-Mart as well.
Some airports have play areas too and that burned off some steam. We also found an open area to run around while we waited to board.
I hope this helps!