International Center for music has probably 30 + guitars for sale upstairs. They are located behind Lulu Hypermarket, near the airport. Address is 39 Ahmed Bin Hanabal Street. They have a really great guitar teacher "Rick" as well. The Center for music is a great resource for all things musical in Doha. They can tell you where to get anything.

Also there is a music store near The Center bus station/souq area. If you go on the corniche from the port towards the airport turn right at the Perfume bottles Roundabout. Go straight through the light and at the RAB do a U-turn. The store is right there facing the RAB on the right.