As far as the cost to furnish a 2 bedroom, I'm sorry I really don't know for sure. I do know that it would be quite expensive as things certainly are not cheap in Qatar. However, a lot of apartments you can rent are already furnished. In fact we did just that. The furniture was all brand new, even still had all the tags hanging off, and the plastic still on!
If you decide to go with a furnished apartment make sure you check out the bed, if you don't like it tell them to do better, I believe that they will!
Good luck to you...
Charlene