L.S.
I once flew by myself when my daughter was 2 1/2 and ds was a few days away from turning 1. It went really well. For my daughter I bought her a new backpack and some new toys to put in it. I put it on our counter a few days ahead of time and told her it was full of new stuff for her. The rule was she could not open it until she got on the plane. She was so excited. She talked about that backpack for those few days, on the way to the airport, and at the airport. I bought her a Color Wonder set, new crayons, and a coloring book. She had just gotten into Polly Pocket so I bought her a small set. I also got her a Barbie doll (cheap one). Along with that, I brought along her DVD player and bought her a new movie. I really didn't spend that much with all this. She kept entertained easily.
DS nursed and slept on both flights. I also had a layover in Atlanta. He woke up when the plane landed in Atlanta and stayed awake until the next flight (less than an hour). As soon as the plane took off, he went back to sleep. He did wake up right before we landed again and I had some things for him to play with.
I also recommend taking a double stroller if you have one. When we landed I was able to strap them both in and just take off at both airports. Above everything else that's what I recommend. I was more worried about keeping up with my kids during the layover than anything. Actually, I had a fear of losing dd in the rush. So it was a peace of mind to have them both strapped in the stroller. I remember flying one time with just dd and running to the next flight carrying her. That was hard with a backpack.
I also brought along a few little snacks for them. Our whole flight was short enough that I knew that would be enough. I also brought along a change of clothes just in case, but didn't need them. Be sure to bring plenty of baby wipes!
L.