If you have health card go to the nearest Health Center, otherwise I would say Al Ahli Hospital

http://www.ahlihospital.com/

Al-Ahli Hospital
PO Box 6401
Doha - Qatar
Tel : +974-4898888
Fax : +974-4898989

Regards!!!

PS: ask any taxi, it will get you there. Or follow the link

http://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=alahli+hospi...

Regards!!