I once in a time used to play for the professional team in Rayyan Sports Club..!
there are various clubs, but it only admits young kids to teach them & build talent that can be useful for Qatar !
hmm, if you just want to play table tennis, i guess, there is QBC near al mannai roundabout, they have a table tennis table there..! i will be happy to practice with you as well,,me being touched the racket about years back now. =P