Pack anything you will absolutely need in your carry on. Like medicines and a change of clothes and your keys and ID.
Be in the gate 30 mins ahead of time and DO NOT LEAVE. People miss flights that way. I just watched a marathon of Airline (a reality show based on SW) and they overbook flights on purpose so as not to lose money. Be aware of your flight times and boarding.
I just flew with our 5 yr old and we had no problems with anything. We took some books and two very quiet toys, but she was more fascinated with the safety manuals. Go figure. We also rolled up a blanket for her and stuffed it under the handles of my carry on where it didn't take up a lot of room, but was nice to have.
Prep for the TSA. Small liquids in quart bags for everyone, and have them out where they can be seen. Kids under 13 don't need to remove shoes, but you do. Etc. That is probably your long pole. You also need to know if getting to your gate might involve a shuttle bus, which can add a delay. I agree with the other posters that more time is better than less. You never know. I once had to run through Heathrow with my not yet 3 yr old in the stroller because we got a trainee at the baggage counter and she took for.ev.er. Had it not been for the family security line (not so common in the US), we would not have made our flight. I actually sent my DH ahead of us because he's a runner. Or the kid needs to pee. Or one of the bags is too heavy, etc. I would MUCH rather be leisurely than in a hurry. One or more of the airports may also have a kid play area, so look for that. My DD really enjoyed the kiddie area in Philly.
Also, find out how meals are handled and if you need to buy in advance, buy to take on the plane or buy on the plane. We either had to bring food or buy what they sold. Only drinks were free.
P.S. In referenced to Julia G's comment - the Bubble Bum is very handy. But it is NOT rated for airlines. We took one for my DD (who is otherwise in a harnessed seat at home) and it was handy for taxis and our rental car, but she did not use it on the plane and she prefers the regular car seat. If they will be traveling a lot by car and have the room, they may want their child's regular seat. The Bubble Bum is for a child 4-11 who weighs at least 40lbs. If they are taking a standard car seat, I suggest the investment in a bag to go over it, to keep it clean on the flight.