I strongly recommend using the seat on the plane, rather than checking it. We flew last spring w/ our then 29 mos old in his carseat, and another girl the same age as him was sitting in front of him, no carseat. Of course, that small, the plane's lap belt does not keep them in place....the little girl was climbing all over her parents, climbing over the seat backs, crawling under the seats, her parents spent the whole flight trying to get her to stay in her seat. DS was strapped into his carseat, couldn't go anywhere, and since he's used to it from the car, he was happy to read & play, and then fall asleep. Most littler kids will be more comfortable in a familiar carseat. Double check that yours has either FAA stickers on the seat or a section in the manual that says it is FAA approved, and be prepared to show airlines personnel if they ask. If she can still fit the infant seat, I'd use the travel system, absolutely!
If she fits in the infant seat yet, (at least 1" of hard shell above the top of her head, AND under the weight limit), then she really should be rearfacing anyway. Even a big 18 mos old is not very safe FF - their heads way so much more proportionate to their bodies, and their neck bones are not fused yet, so their necks stretch out too far in a forward facing accident which can cause severe damage to their spinal cord.
Google joel's story, internal decapitation, and extended rear-facing for info if you'd like to keep your daughter safe in the car.