LX so far the only shop where I have seen wetsuits is Go in Villagio Mall, but in the area nearby the Museum of Islamic Art there are two or three stores you might want to check because they sell marine stuff/goods.

Also going to Al Wakra there is one store for marine items. When going to AW from Doha, passing the first R/A on your right hand side there is a store for marine items.

Do you know where the Lufthansa offices are (Rayyan Complex) there you can find another store that sells maritime stuff.

Hope to be helpful!!

Regards!!