Yep, we're crazy.
But really, it's not that bad. I mean a few hours is NOT that long. Honestly, none of our flights have been bad... our girls are great and often sleep. Definitely get a portable DVD player if she'll watch anything (mine wouldn't at that age, but I'm sure some would), bring new toys, have lots of snacks available, bring books, don't be afraid to softly sing silly songs, and try to make the best of it. 


We're taking her touch and feel books, a DVD player (although I don't think she'll wear the headphones), some snacks, and some window clings. I also planned our flight for right at her normal nap time, so I hope she sleeps!
If she won't wear the headphones, you may want to re-think bringing along the DVD player. Unless your daughter will watch the pictures without sound. You are supposed to use headphones on an airplane for any gadget that makes noise. If you use the DVD player without headphones the FA may make you turn it off. And if another passenger complains, they will make you turn it off.
I think it would just be easier on you to not have the DVD player there, and have a child that can't understand why they are not able to use it.
That would probably work great for a kid who will be happy in their seat for 2.5 hours (the length of our flight). Our 17mo would *not* be happy, unless she managed to fall asleep. In a car, we could (and do) stop and pull her out to let her have a different position, etc. If I do that on a flight, there are 2 consequences I'm not happy with:I have to agree with the others who said to buy a seat. Kids are used to being strapped into car seats and know that they have to stay seated and buckled, it's the rules. But holding a child in your lap, they do not understand that they have to stay seated. We flew once with a little boy in front of us who spent the entire flight leaning over the back of the seat, drooling on my DD. Every time the parents tried to make him sit down, he would scream, so up he would go. If you absolutely cannot get a seat (they are often 1/2 price for under-two's) then make it very clear that they HAVE to stay seated.
Personally I would never let my kid ride in a car without a car seat, so the same goes for a plane. I was on a flight once when a little girl seated in her dad's lap hit her head on the ceiling during unexpected turbulence. I said right then that I would never take that chance when we had kids, and I never have.