My son is almost 3 years old, and he has been on plane flights since he was 2 months old. We always take 1 backpack that has his goodies in it....a portable dvd player (a lifesaver!), his favorite toys that are easy to keep at a chair, snacks, and his own cups. We do not take his carseat on our flights with us, except as baggage. We've never had any problems, and everyone always comments on how good of a kid he is on the flight! So just bring your little one enough to keep her busy...and if you have a portable dvd player...definitely use it! Good luck!
P.S. I just read everyone else's responses, and I'm actually bit shocked at the amount of people who drug their kids for the ride. I'm, by no means, someone against medicine, but this just seems unnecessary. Also...the people who are saying it is FAA regulation to have a carseat....like I mentioned before, we've taken our son on many many flights, and never once had to use a carseat. We check our carseat every single time, and have been on different airlines also, so I can't believe that this is true. So make sure and check into that before you lug that thing on with you....