If you travel alot I suggest investing in a Sit-N-Stroll. It's a carseat and stroller in one. The weels collapse into the bottom of the car seat and the handle retracts in the back of the seat. It's a carseat that is approved for the airlines and use in USA, Canada and Europe. I got mine at Target but you could Google it. This stroller fits down the aisle of the plane and you can use it in their seat or put it in the overhead if you are having you little one in your lap.
Make sure that your daughter is feeeding as you climb after take off and when you are decending to land. Their ears are small and the altitude change that pops your ears at about 10,000 feet hurts them. So make sure she is sucking a bottle or being breastfed.
Waht to take on the plane...Take changes of clothes. I always stocked up on diapers and awipes. Also, on whatever food/snack she was on at the time. You never know when you might get stuck at the airport, have a delay in flight etc. I also brought picture books and her toys. Bring a surprise toy that she has not seen before that you think she'll be facinated with. Mine liked anything that made noise! LOL!
Ask for the Bulkhead seats so that you have plenty of room and on some lights there is a bassinet you can get when it comes time for her nap. Ask about it when you are making reservations.
Good luck and have fun.