You just have to visit NATIONAL HEALTH AUTHORITY who are responsible for issuing MEDICAL LICENCES to doctors or practitioners in Qatar
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http://www.nha.org.qa/moh/En/index.jsp?
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I only know that you have to go through EXAM of Qatar standards and if you are passed then you will be given permission to practice in Qatar.
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Its location is opposite to WOMENS HOSPITAL or adjacent to LULU Center on Rayan Road