There are 2 schools of thought on how to move the carseat through the terminal. I prefer the backback-style satchel that leaves my hands free; the satchel is available at BRUS. There's an Eddie Bauer branded model, and one from Prince Lionheart; they are very similar. The trick to wearing it correctly is to flip the straps over and under the back side, so that you can wear the satchel with the "seat" of the carseat next to your back. It's higher that way, and won't bang against your legs.
There is also a school of thought that prefers rolling it through the terminal bungeed to a rollaboard carryon, or to the stroller. If your child is little and tends to fall asleep on planes, you can also just prop the seat with the child in it onto the fully-reclined stroller, and then bungee them both on to secure it while you roll it through the terminal to leave the airport. Run the bungee in a fig-8, under the seat of the stroller, cross over the carseat, and then hook it behind the reclined back of the stroller. Warning about bungee cords: try to get the kind with plastic end-hooks, b/c officious TSA agents will sometimes hassle you about bungee cords with metal hooks. (Bungees are not on the prohibited list, but sometimes these folks get a bit ahead of themselves, and they don't like it when you argue with them, however politely.)
Note that if your airport uses sizing templates on the x-ray machines, most carseats will not fit through. If this happens, the carseat will have to be manually checked by a TSA agent. It is OK if it does not fit through; carseats being used on board are NOT subject to the carryon size limitations.
