Let me see...

On al waab street and behind Khalifa Stadium you have Aspire Clinic which specializes in sports medicine, but anyone can attend by paying the fees for registration and consultation.

Another choice would be Al Alhi Hospital which is not that nearby al waab but is a good one.

Also you have HMC, if you are comming as an expat you are entitled to get a healthcard (paying the fees) and then you have "free" medical attention.

For additional info check in HMC

http://www.hmc.org.qa/hmcnewsite/

and in

http://www.ahlihospital.com/

Regards!!