Can't vouch for all children everywhere, but all the Western kids I know, or know of, here are happy enough. The American school makes a good social base for parents, as well as kids, and there are sports and bands and dancing clubs and theatre activities and everything a conscientious soccer Mom could want. It's worth noting that a Westerner can go for days without hearing Arabic spoken or meeting a Qatari face to face, which is how most Qataris prefer it. Substitute Spanish for Urdu or Tagalog, and it wouldn't be too different from many American cities, I should think. Except safer, of course: No guns and not much narcotics.
Mind you, I'm Brit so what do I know?