You can go for Medical any day from the date of arrival
Medical is also takes a max of 30 mins to 1 hour depends.
u should go to the gate for EMPLOYEES (the back side of the Medical commission office), show ur visa copy, they will direct you to the Cash Counter there u have to pay 100 QAR as the fees.
The cashier will be taking your photo so be handsome then... lol...
then u have to go for the X-Ray, and then Blood Drawing,
its in the near by rooms, if any doubt ask the ppl in the reception.
the X-Ray and Blood Drawing is on First Come Fist Serve basis.
Once this proceedures are over, the details will be available in the CID office in four or five days. So wait for one week, then u can go to CID office directly