Your son absolutely needs to be in a harnessed seat (properly installed) for his safety. Even a little bit of turbulence can do a great deal of harm to an unharnessed child. The lap belt, on the airplane seat itself, can cause just as much harm. So, using a child-friendly seat is important...besides, he'll sleep better!
Do not check your carseat (your child should be riding in it anyway). Airlines are not careful with luggage and could damage the seat causing it to lose effectiveness in a crash.
If you don't want to lug a big seat around. A good, inexpensive, FAA approved carseat is the Cosco Scenera (5 point harness version). It rear-faces to 35lbs and forward faces to 40 lbs. It's very lightweight, so will be easy to carry and relatively easy to install. It can be found at WalMart, some Targets, and some KMarts for around $40 dollars.
This information is copied from a thread on car-seat.org for flying with a child and carseat
For others who are flying:
I flew last week on Continental and had no issues. However, this is what I brought in preparation:
1. 14 CFR 121.311 Seats, safety belts and shoulder harnesses
http://ecfr.gpoaccess.gov/cgi/t/text/text-idx?c=ecfr&...
I went through and highlighted some of the relevant parts where it says that they may not prohibit use of a seat if you bought a ticket.
2. I also had my manual and marked the pages where it said it could be used on an aircraft and that it must be rearfacing (SS1).
3. Continental does not have a CRS use policy on their website, but many airlines do so I would print that out and bring along. This is the Hawaiian Airlines policy, for example: http://www.hawaiianair.com/Services/...-toddlers.aspx
If it is questioned, remain calm, ask for policies in writing, ask to speak to the pilot and all else fails, ask them to call their corporate office for clarification.
If you'd like to ask this question in a carseat forum where there are many, many helpful carseat techs go to http://www.car-seat.org/forumdisplay.php?f=2 It's a great place and you don't have to register to ask your question.
Happy traveling!