ASD (the American School) is excellent

Family and social life will depend largely on your compound and your employer, but Qatar is generally safe (except for the driving) and a single mother from the West should not expect have much difficulty negotiating life in Qatar. Qatar is conservative but generally not closed minded.

Lifestyle, again, will depend largely on the salary and benefits package offered by your employer. This really is essential.

If you can be more specific on who your employer might be--one of the American universities in Education City, Qatar University, etc., people could be more specific about the work environment, benefits, housing, etc.

Good luck.