Don't do it. They are heavy and bulky and take up a ton of room on the plane. If the person in front reclines she will be even more smashed. If you do it the car seat HAS to go on the window seat and you must purchase the seat the next to it, which will make you all more cramped.
There really is no need for it and honestly you don't see many in car seats on planes pass age 2-3 and even then not that many do it for the younger.
We flew with my DD at 20 months and she had her own seat and no car seat and was fine.
It really is not that worth it.
Most children on most car trips would also be perfectly fine without a car seat. We use them to prevent tragedy for those occasional times when we are in a collision. While air travel is safer than car travel, when airplane accidents do happen they occur at 150-200mph (that's survivable runway incidents during take-off and landings as they are more common than the dramatic fall out of the sky unsurvivable crashes). Car seat use has increased dramatically on airplanes. So while many parents still don't use them and many parents still travel with babies on their laps, more and more parents choose to protect their kids just in case.