NHA (Now Ministry of Public Health) is the government body looking after the health issues:
Following is the link:
http://www.nha.org.qa/jsp/content.jsp?menuId=8
another private hospita :Al Emadi Hospital.
http://www.alemadihospital.com.qa/site/
American Hospital in Doha Qatar:
http://www.ahqatar.com/index.php
Al Ahli Hospital Doha Qatar