Its not available ONLINE to download it. You have to go to ur nearest HEALTH CENTER and they will provide u health card within 15 minutes. Here is the link, click it to know more
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http://www.gov.qa/wps/portal?New_WCM_Context=/wps/wcm/connect/cnt/en/1_h...
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But you can renew HEALTH CARD or get a duplicate {lost/damage} online but to have a brand new one you have to go to your nearest HEALTH CENTER