W.L.
I traveled a lot the first year of my sons life. I would suggest holding her, but taking her car seat and checking it as luggage along with the stroller. Do you have a carrier (ergo was wonderful) for the plane ride. She is not going to want to stay in the car seat for that long save the money. If you still nurse I strongly recommend nursing her as the plane takes off and lands to help prevent pressure build up in her ears. I also recommend Oregon's wild harvest children's ear drops top help her ears during the plane ride http://www.oregonswildharvest.com/owh/browse/product/chil...
Also take lots of snacks and things to distract her, but also know that it is okay if she gets unhappy during the plane ride she is still a baby.
Have fun.