i dont know whether they give you a medical before you leave, probably depends on the company, your seniority and your age.

But the aids test nad other blood test will be done after you arrive in Doha, usually within a week or so arriving, they do not do anything in the airport. The test is done as part of your clearance to get a residence visa and to get an i.d. card, it is not as daunting as may you think.