D.C.
Don't be afraid! I fly with my kids all the time. They love to fly on planes (ages 6 and 3). Buy a seat for your child, and then you can take your car seat on the plane so she will be comfortable just like in the car. She may even nap if that's what she does in the car. Bring snacks, stickerbooks, and even a portable DVD player if you have one.
Kids this age are too young for gum during takeoff and landing to pop their ears, so I bring a sippy cup (buy a bottle of water or juice after you go through security to fill it) and lolly pops to suck on.