Parahawk,
I don't think you need to worry about that. Expat wives do get jobs here without too much trouble. There is a need for all types of professionals in fast-growing Qatar. The respect issue I find is quite the opposite to what your wife is concerned about. My wife has always been respectfully treated here both by locals and other expats. It seems like women do have a "protected" standing in society, even if they are foreigners (and dressed like foreigners). I definitely don't see the "second class citizen" problem you mention, though I'm sure there are exceptions, so let's hear from others to get a balanced picture.
I must say, in general as foreigners we don't enjoy equal treatment under the law. If your wife has a car accident with a local, she will probably get the blame, regardless of the circumstances. Accept it and let the insurance company handle it. This is a battle you won't win.
Best of luck.