I agree. Historical sites are a rarity in Doha itself (much too young), although there are some interesting spots within a couple of hours drive--a bit out of your way and not the easiest to access. The Museum of Islamic Art is by far the best Islamic cultural site in Doha. It is world class and centrally located. The opening hours are somewhat odd, so check before you visit.

http://en.wikipedia.org/wiki/Museum_of_Islamic_Art,_Doha