Your situation is tricky, i think to avoid unlikely localities you need to be in pearl, westbay, alwaab but your 6-7K budget quite less,
so better you make it 10-12, or possibly share a flat in westbay for that money.
however if you're Allergic to Indians (Pakistanis, Bangladeshis, Nepalese....) i suggest you drop idea of coming to Qatar, they're everywhere :):)