Definitely check out QAWS, and also the Animal Care Center run by Dr. Paul, not far from DESS, near Markhiya R/A - tel:4877144. I know there is a beautiful pup there now that he is housing, unsure of breed (tho she looks like she'll be a medium-large sized dog, not a small one).

You should also check the ads people put up in the supermarkets around town -- usually there are loads of ones for animals (both old and new) needing good homes.