Welcome! I have no idea what companies may be doing shopping there but you might check Bare Int'l [
www.baidata.com] and Gapbuster at [
www.xec.gapbuster.com]
I did a Google of "Mystery Shop Dubai" and got a fair number of hits. Use your good judgment about whether an advertisement looks legitimate before you sign up. Reasonable 'standards' in the US are to not send personal information by email but sign up with a legitimate looking website. Here we also tend not to respond to emails soliciting us that are not from a corporate email address. The reasons for this are the danger of identity theft and scams. In your research you may even find a forum of shoppers who shop in your area.
I don't know that any of our lists of companies that do shops will help you, but you may want to look at the lists on Volition.com because they usually have descriptors of the types of jobs companies do and sometimes the locations.