notaflygeek welcome to the QR forum.
I cnnot give definite answers but I would imagine that The Bumble Tree and WHSmith are the most likely places. I have seen some aircraft models in WHSmiths but I do not remember what.
If you use the maps on
http://dohahamadairport.com/airport-...e-airport/maps especially the 'Duty Free Plaza - South' you should be able to find the shops fairly easily.
I am sure that your son would love some of the play areas dotted around the airport.