Of course there are diving clubs here. You might want to check out Pearl Divers - that's a PADI centre on Al Merqab street near Doha Clinic, 444-9553. They organize dives every week and are generally cool people :^) Ask for Abdul Latif and I am sure he'll be glad to help you out. Hubby is diving with them and he has pretty much the same experience and qualifications as you and he likes it, so maybe you could dive together.

Cheers