Trust me.... take the carseat. He, and you, will be so much more comfortable.
I've flown several times with my kids as they've aged. It was a far more relaxing trip when I could safely strap them into their carseats on the plane. In the one case where I forgot the carseat, DD3 was able to easily slide right out of the latched belt of her aircraft seat. Most carseats have a sticker on the side that says "approved for use on airplanes" or some such... just make sure yours has that sticker!
We also take a bag with lots of different things to keep the kids occupied. At 2 years old, it was usually snacks, crayons and coloring book, a couple favorite reading books, a few cars, some small action figures, etc...