Hello, C.!
Never underestimate your daughter's ability to understand, even at two years old. Talk to her in advance about what it is like on the plane, what she will see, and that there are other people on the plane who could be sleeping or reading.
Engage her as much as possible . . .it works so much better than expecting her to behave on her own. Read stories - some of the best ones are books that have something to look for on every page. (I SPY ones are wonderful - they have ones for toddlers.) Pack a backpack with activities. DO you have a quiet book? You may find one online - my mom made them for my kids - fabric pages with things to do like buttoning, zipping, counting, braiding, etc. Worth an online shopping trip!!
Pipe cleaners are cheap, quiet, and can be twisted into all kinds of fun things - - I brought these on plane trips when my kids were little. I also brought toys that came with Happy Meals or little inexpensive playthings . . . not a big loss if they were left in the seat or dropped on the floor and overlooked.
Of course, there is always the portable DVD player and/or CD player. When mine were this age, we had read along books with CDs. My boys are into Nintendo DS, but are much older now. . . I use sparingly, but it is WONDERFUL on plane trips.
Don't forget something to suck on or chew for take off and landing to help her ears. Talking about that ahead of time will make that sensation less scary for your daughter. Watch for signs of runny nose or cold symptoms in the days before flight and try be sure she is WELL on flight day. If she is having any kind of nose or sinus issues, carry meds to minimize discomfort, especially on take off. Be sure to get travel size and have in ziplock bags - - security, you know!
Going through security can be frightening - - and the whole "take off shoes" thing is a big job with a little one. Explaining it to her ahead of time, and talking to her through the process will be a big help.
Snacks, of course!! Juice boxes are much neater than getting drinks that are served on the plane. And, just in case, carry gallon ziplock bags for messy or stinky clothes if a change is necessary. Double bag so odor is minimized.
Good luck!