Definitely do the carseat thing. You will go crazy trying to hold that baby all the way home, especially if someone is crammed up next to you. He should sleep much better. You will have to buy him his own seat though. Good luck. I'm trying to decide if I want to do the trip home by myself with a (will be) 9 month old and a 3 year old this summer. The heat of Doha verses a hellish ride home...

One trick if you do take the carseat -- to carry the seat through the airport, turn it upside down, put it on top of your rolling carry-on bag and get a big bungee cord to strap the seat on to the bag. Saved my life!