Try the Berlitz Language Centre. According to their website, (http://www.berlitz.ae/courses.php?dat_id=14&cor_id=20) they have Dutch classes.

It's a villa with a blue sign...

Berlitz Doha
D. Ring Road, Al Hilal West
P. O. Box 23605
Doha-Qatar
Tel: 974 4550506/07
Fax: 974 4550503
Email: [email protected]

Director: Mrs. Frida Saadeh: [email protected]

I've met the director before - she's quite nice.
Hope I helped! :D