E.H.
I've traveled alone with my daughter a lot, so I'll share with you a little of what I learned.
1. If she'll walk or ride in a carrier, I would recommend using that. Security makes you take your kid out of the stroller, fold it up, and put it on the x-ray machine. It was really difficult to do that and make sure my daughter didn't run off. Also, you have to find elevators every time you change floors. The stroller ended up being a bigger hassel than a help.
2. The car seat is big and bulky, but you have two choices when you check in. You can ask them to check it for you, or you can see if the flight as any extra seats (assuming you didn't buy her a seat.) If it does, they will usually let the child ride in the car seat in the extra seat on the plane. This was a life saver on late night flights for us.
3. Ditch the diaper bag and put everything in the biggest roller bag you can get on the plane. The goal should be to carry nothing exept the kid and roll the suitcase. That way you have free hands and everything you need in place. This helps a lot for holding onto your daughter and tickets/passport/ID, etc. through security and on the plane. Also, you can balance the car seat on top of it if you're taking it on the plane.
Hope this helps! Happy travels.