[sabriyetj]

I know of no shops here in Dubai that sell good prof. costumes. There is however, great fabric (along with the fab jewelry mentioned above) to be bought in Naif Souk and also a district called Satwa. In both areas you can find tailors who are great at duplicating anything that you bring them, but they don't do emroidery. If you plan on doing this while on a visit, I recommend going there early on in your trip so that you allow time for your item to be made and then perhaps fixed if it's not how you wanted it.
There are also many dancers who sell costumes and I do know of a man who sells some Lebanese professional costumes out of his home. If you want more info on getting in touch with him or with dancers who might be selling stuff here you can PM me.
Best of luck to you!