Since I'm a car seat tech I am a bit biased...but we use a car seat on the plane every trip as long as our kids are using seats that can be used on the plane (ie, dd was 6.5yo on our last trip and her seat isn't FAA approved so she doesn't use a seat on the plane now). The last time we flew before this past December, dd was 3.5yo and she slept almost all of both flights in her car seat!
Ds was just 2yo during our December trip and we found it really easy to use his car seat on the plane... rear facing even! He was riding in a Britax Boulevard at the time and it fit really well in the airplane's seat.
There are lots of ways to get the car seat through the airport. OR.. to forgo the car seat altogether.
Go Go Kids makes a travel cart for car seats. It is pricey though at $79 on
Amazon.
The Traveling Toddler is less expensive at $14.99 (also at Amazon), but you need to use your own wheeled carry on.
The Samsonite Micro Mover luggage cart is an older option (and what we've used for the last 6yrs) and about $25. The bonus w/ this is that it collapses easily to store in a backpack or other carry on.
Collapsed:
Extended:
Lastly...the CARES harness. This is NOT a car seat but a harness specifically designed for airplane use. This is a great option for a family that flies often and does NOT need a child restraint at their destination. The harness costs about $75 (at the CARES website) but you can also "rent" one on eBay.
The CARES harness can only be used with children between 22 and 44lbs and there have been some reports of younger/smaller children submarining a bit due to it not having a crotch strap.
ALSO... here is a
great website w/ a TON of great info about using carseats on airplanes.
HTH!