Not that I know of, you can usually find property for sale in the newspapers, but if you are a foreigner you can only buy in a few selective developments in Qatar. The Pearl development has a website www.thepearlqatar.com but it doesn't show prices and availability, you have to call them and arrange to see them.
You can see Qatar resale property on some international websites, look at

http://affiliates.themovechannel.com/fish4/Property/results.asp

and quite a few on:

http://www.rightmove.co.uk/overseas/qatar/ad-dawhah