I have traveled a couple times on a plane and had layovers and waiting to board with the kids. Since you have one it will be easier (still can be a headache). I traveled with my friend, her daughter, and my 3 daughters on a plane trip. I think we did it pretty smoothly. I had one on my lap (my 7 month old at the time) and 2 (my almost 2 year old and 4 year old) in seats at that time. My friend had her daughter on her lap.
When I went, I packed as light as I could. Having checked luggage is easy if you have someone helping you get it checked in and picking it up.
I had an umbrella stroller for easy transport through the airport (some airports you have to walk). If you are not taking a carseat it would be good. If you have a car seat and a carryon...you can look online, they have straps to hook the carseat onto the carryon as a stroller. Your carryon would have to be a good sturdy one if you choose that option. We had a rental car waiting with carseats at our destination so we didn't bother with having a carseat.
If you take a car seat, you have to make sure it is FAA approved. If not taking one, it might be easier for her actually lay down in the seat, she can sleep a little better.
I had a backpack with our carry on stuff on, so I could sling it on, and my hands would be free if I needed to carry someone. Like others had said, new toys are good. Magna Doodles, or Aqua Doodles, snacks, her sippy cup, favorite blanket, or something like that. Portable DVD players, with a new movie or her favorite or if she has a favorite CD she likes, a CD player would be good with headphones so you don't disturb your neighbors. I personally like the View Masters, and you can get lots of different pictures...we have dinosaurs, animals, Dora, Carebears.
You can make some silly putty or goo too that isn't too messy or playdoh too. Playdoh comes in little gift favor size so that is all you would need. You might have to check with the airline to make sure that is ok to take on...But that provides a lot of fun for a kid. We have a picture book of friends and family you can easily make up with your own. And it benefits if you daughter hasn't seen her grandparents in awhile, she knows who they are.