I am not sure that it is the best sporting activity but definitely it is the most practiced one in Qatar : SHOPPING...the malls are quite big and you can do quite a lot of km going around shopping with the advantage of being indoor with AC :-)

If shopping is not your cup of tea (I can understand), do not worry you can find nearly all sports here (expect winter ones :-). Golf, Martial sports, Tennis, Sailing, Squash...you ask.

Many hotels (Ritz, Four Season, Ramada Hotel, Sheraton, Intercontinental...) have a yearly membership to access all there facilities plus you can find independent gyms... and a lot of compounds offer as well facilities to their residents.

Well just in July I would advice you to start with indoor sports :-)

Welcome to Qatar :-)