M.B.
If you're breastfeeding, try to get a window seat and nurse on take-off and landings - that helps tremendously with ears popping and my younger son would just fall asleep and would usually sleep most of the flight. If you're not BF, just giving her a bottle or sippy cup at both those times will also help.
If she does seem to want to be awake, I recommend walking around with her as much as possible. I travel alot for work and it amazes me the number of people that seem to think it's okay to let a child scream the entire flight.
Also, I would bring along new, small toys - those can be a great distraction, as well as any favorite toy or comfy item from home.
We traveled extensively with my two boys from the time they were 9 mos. old and never had any issues. Indeed, due to my nursing "trick", we usually got wonderful complements on how well behaved my boys were.
Tylenol might help, but if I were to give a child anything, I'd given them Benadryl - that puts my whole family to sleep pretty quick. I have a friend whose a nurse and she's says that's perfectly safe, even with frequent use.
And, finally, if your daughter senses that you are nervous about the whole experience, that will just make her that much more nervous. You need to relax, plan to get to the airport early and if she's walking let her run off some of her energy, or at least bring a blanket you can put on the ground and let her play for a while. Keeping her in a stroller, for example, the whole time before the flight will only increase her desire to be active once you get on the plane.