Great idea, but only if you have bought a separate ticket for your child. I took my son often on airplanes and always took his car seat. I took an umbrella stroller which will help you in lugging it around the airports. Another plus...once you get to your destination, you already have his car seat for the car trip from the airport. There was some talk at one time of airlines making it mandatory for children under a certain age and/or weight to be seated in a car seat while on board. It never became a requirement but is a great idea. The only problem is that the airlines allow you to hold your child in your lap to avoid having to buy another ticket. Unfortunately, this often makes it extremely uncomfortable for other passengers sitting in close proximity. Although it can be quite expensive with several youngsters, I vote for buying the extra ticket and taking the car seat on board.
Be sure to take some snacks, books and toys for your child to use on the plane. While taking off and landing be sure your child has something to suck on to help with the air pressure in their ears.