My experience is , a car seat at that age was great. I think they sale car seat "back packs". They make lugging the carseat around look more comfortable.
My vote is take the car seat. It wasn't until she got alittle older, and didn't want to sit in her car seat, that we started checking the seat.
Good luck.
I would take a car seat on the plane for a two year old. My two boys both did much better in a car seat on the plane since they were used to being in it in the car. I think it was kind of a comfort thing. After kids get to 3 or so, their legs are getting too long and hit the seat in front of them if they are sitting in a car seat.
I'm not sure of anywhere that it says a car seat is not recommended for a two year old on plane.