well, I personally do not know of a country that just accepts an other countries medical straight across the board. (some countries within the E.U exempted of course).
Qatar Airways is governed by the QCAA and requires a Qatari Licence and Qatari Medical to fly a Qatari registered aircraft.. just as you would have to do in any other country in the world.
having said that, the medical is just a Standard aviation medical.. nothing extreme and no suprises.
Poisoned by Compromise
Krunch