For 2007, your foreign income up to $85,700 is excluded from taxation(this is called the income exclusion). It will be increased by a number for inflation for 2008, but I don't know that number yet. There is also a housing exclusion. Even if your employer pays for your housing, it will be considered part of your total income just like it would in the US. The exclusions are literally entered on your tax form as a negative income.

Your income bracket prior to the exclusions determines the tax percentage that you would have to pay. You will probably be in the 28% bracket, as this covers a pre-exclusion income of roughly $80,000 - $165,000.

I'd check out Publication 54 on the IRS website to answer any other general questions, but you may want to talk it over with your accountant if you trying to determine if a move to Qatar would be advantageous or not.