My kiddo who is almost two has jet setted all over this country and internationally.
Here are top things for travel:
DO not bring the car seat, it is way too big for the seat and will interfere with your comfort. If you purchase a seat for your baby or are lucky enough to have a vacant seat next to you, you can sit her up or lay her down with a blanket. The two of you will be much happier with the space.
On take off and landing, it is vital she have something to suck on to stave off the pressure: a pacifier or drink will suffice. If you want to go the distance, there are these things called "Ear Planes" (available at drug stores) that help with pressure issues. I would still have her drink or suck.
Hydration: it is key to keep her hydrated. Offer lots of liquid.
Infant Tylenol handy just in case
DON'T be timid of walking around with your baby up and down the aisle and take advantage of the larger space near the bathroom at the back of the toilet.
Remember to prepare yourself for security. It's a pain in the butt especially if you're doing it alone but be organized and it will help. Put your liquid (her drinks, medicine) into Ziploc bags and be sure to let the TSA person know you have them.
Happy Flying!