R.D.
Buy the seat. In the event of any kind of plane problem, he will be much safer in his carseat. Read the account of a woman who is trying to hold onto her child and he is ripped from her hands. She survives, her child not. That was enough to do it for me. I know you don't want there to be a plane problem, but you never know. The only reason to use carseats ever is to protect your child. Also, I assume your child is used to riding in a carseat in the car. It will be more natural for him to ride in the carseat in the plane. Might be easier to keep your daughter in her seatbelt if her brother is trying to run free. Trying to keep a squirmy toddler in arms for over an hour is no fun for you or the other passengers. Plus you will have the carseat for when you get to FL, and you will need it while in FL. You will be able to load the plane first since you have a small child and can get the carseat positioned then.
Have fun on your trip.
R.