I bought a large, lightweight duffle bag and used that to carry DS's car seat to the gate. Once we got to the gate I put his stroller in it & gate checked it. It was waiting, in the bag, with the other strollers, when we got off the plane.
I wasn't going to put it in the bag, but I asked at the gate, and they asked one of the bag handling guys & he said definitely use the bag! I guess they get knocked around a lot.