Balhambar stopped serving Qatari food a few years back and has since just served Lebanese food.

The shop on airport road is good.  I have only ever eaten their food during Ramadan, with other Qatari friends who assure me it is very authentic. 

I heard that there is a place on Salwa Road somewhere after the flyover but before decoration roundabout called Gulf Star of Khaleeji Star or something, but I've never managed to find it. 

Not sure where else you can possibly find true, Qatari food.