The University of Qatar's graduate admissions page is here. Note that they do not admit PhD students in physics.
The Hamad bin Khalifa University's graduate admissions page is http://www.hbku.edu.qa/en/DynamicPages/index/139/hbku-admissions [Broken]. Note that they do not have a PhD program.
That appears to exhaust the possibilities. There are various western universities with satellite campuses, but you'd do better to apply to those institutions directly as my impression is that their activities in Qatar are limited to certain subject areas (principally archaeology and arabic studies).