I know qatar really needs networking gurus as networking is a relatively new field in qatar and I also know a place where they are urgently looking for IT people but the only problem is that the hiring manager there is hiring only those who are from his country of origin. So i will not be able to help you out. But for starter try applying to the Pension and Retirement Authority. its office is opposite to the Gulf Times office.
In order to get a job in qatar you need Wasta so better luck finding some Wasta