There are lots of people with pets in Qatar - I don't know of any specifically in Al Khor but there will be some there too no doubt.

One big issue to check is if your accomodation will allow pets (get it in writing).

You just have to keep your dog under control and avoid locals, other Arab nationalities and many Indians -they are mostly just ill informed as to whether dogs are dangerous or diseased - I would do the same with my pet in my home in North America - not everybody likes or is comfortable with dogs.

It gets very hot here for 4 - 6 months of the year 50C+ so you will have to take the dog out very early in the morning to get some exercise and only for short times during the day as the ground is very hot.