Doha Art does printing on Shirts and many other things. I am not sure about embroidery though.
We get our work shirts printed there have been no problems of peeling or fading with the prints.

They will do samples for you at cost so you can see the quality.

They are in Al Saad, near the signal with Nissan.
It is inside the shopping complex so you won't see it from outside.

4444-1490