At 1 year old, it could be a good thing to have that carseat, especially if your son falls asleep in it normally.
I had an awful experience bringing a 2 year old on a plane with a carseat. He always fell asleep in his seat, and we scheduled our flight (to Chicago) during his nap time. The first bad thing that happened was that our flight was delayed 2 hours. Then we get on he plane only to realize that his carseat only made his legs that much closer to the seat in front of him, allowing him to kick it constantly. The flight attendants would not take the seat (we were using a Britax Marathon). I was able to turn the seat sideways, but the flight attendants wouldn't allow that for take off or landing. He threw an absolute fit. The girl in front of him was not happy either.
On the way back, we gave him benadryl and he slept most of the flight (that was a plan that was OK'd by our pediatrician). We checked the carseat.
My sister in law just flew cross country with their 3 year old and thought they'd bring their carseat for the same reasons. They flew Continental only to realize that there is less legroom on those planes - the carseat barely fit.
It may depend on the airline, but I would check with them and their regulations.
Good luck!