110% bring a car seat. Even if you can get away without it based on weight or age or whatever, your child is used to being in a car seat, buckled, in the car, and this will be familiar. They might even doze right off to sleep like our LO does every. single. flight. before we are even wheels up. We strictly do not let her out, unbuckled while on the plane, unless we have to do a diaper change. Same with the big kids, so she sees their example. Just like we would never let her ride unbuckled in the car, she doesn't know any different. Babies become projectiles in turbulence.
We bought a Cosco Sceneca from Walmart for about $39 and it is the best airline travel seat ever. It weighs NOTHING, seriously it is so light and compact, I just plop it right on top of our umbrella stroller and wear the baby through the airport. You can easily tuck the latch straps in so they aren't projectile weapons every time you turn around, and it fits so easily in the narrowest of airline seats! It is probably not the high safety rating for vehicle crashes ever, but your goal in an airplane is really to keep them from flying through the air when there is turbulence. Also you do not need to rear face like in the car unless you are using an infant seat or your seat requires it to a certain weight. We had ours forward facing when my daughter was about 14 months, because it fit better forward facing, she could see the in-seat tv, and you aren't really worried about the forward force of a head on crash in an airplane. In a lot of airplanes, if you rear face then the person in front of you cannot recline, so some people rear face on purpose to prevent them from reclining and getting kicked the whole flight. (Recliners just get kicked by a 2 yo in my world lol, sorry, your choice)
