We travelled with our then-16? month old on the plane.
We did NOT buy a seat.
We checked our carseat.
We don't even own a stroller.
And brought few toys.
And it went very well.
We bought this thick plasticky carseat cover with handles and zippers, and it was just perfect. Made it simplesimple for my pack mule, er, husband, to carry to check-in.
Had DS in the sling (non-ring-sling so I didn't have to worry about setting off the metal detector).
Had a few toys, but as usual he did better just looking all around and playing with the things in front of him, than official toys. Official toys get thrown; airplane safety seat cards get looked at, put away, pulled out, put away, pulled out....and so on.
He nursed and nursed and nursed some more. We didn't get off the plane, but the plane did have a stop halfway down, so that was a bit rough on the ears. However, out and back, people kept commenting that they didn't even know we had a baby with us, he was so quiet (he just made up for that last weekend on a train trip, though).
Here's my reasoning on the carseat/plane-seat thing...the theory behind using a seat on the plane seems to be *not* for crashes, but for turbulence. However, my son would NOT deign to be strapped into his seat during the flight, so he'd be up and out in a time of possible turbulence anyway. Just like I undo my own seatbelt once the light is off, I'm quite sure DS would want that too (even once he HAS to have a seat for himself). So...for the time that he doesn't need his separate seat, we're not making him. For me, the reasoning just doesn't track logically.
Oh! This worked well for us, too. Although DH is on the bigger side, with a Buddha belly, he agreed to be in the middle seat while I took the window. That way my bare back and side was blocked by his belly when I nursed DS on one side, and blocked by the side of the plane/window when I nursed from the other side. I'm usually not one to use the restrooms on the plane anyway, so it wasn't that big a deal. (Before having DS, though, I always wanted the aisle seat b/c I'd rather be interrupted than have to interrupt someone else on my way out of the seats) Anyway, the him-middle / me-window arrangement worked well for us.