See discussion under 'Preparations and Set up". http://www.qatarliving.com/taxonomy/term/50. Despite the above remark, there are a lot of happy families there. For a carless mother of young kids, Al Khor would be far better than almost any compound in Doha.
The worst bit of a commute would be getting out of Doha: not too bad if you're in the North of the city. Once you're clear, it's only about 40 minutes.
But see also threads on accomodation. Situation's murder in Doha at present. Suggest you stay Al Khor to begin with then if you don't like it, move to Doha after the Asian games have finished in january.