I am a SAHM although my children are all teenagers so I could easily work if I wanted to. I choose not to though, because I like the flexibility of being able to come and go as I please, and I like to leave for the whole eight weeks over summer.
If I could find a part time hobby job that I loved, with no hassles that fitted in around my DCs school hours then I might take it, but at the moment I have no desire to work! Also as a local hire the salaries are not great and we tend to get priced out by Asians/Filipinos who will work for much less. Having said that, some people do specifically want native English speaking women with strong written English, and UK/US experience so there is always a job if you want it.
If you are very outgoing and sociable there is always something to do and someone to do it with, but you have to make the effort to put yourself about a bit in the early months, until you get a network of friends going. It can feel a bit like speed dating at first, but eventually you will click with a few people and will start to feel less contrived, if that makes sense.
We are very happy here. It comes with its challenges, to be sure, but the lifestyle can be fabulous if you throw yourself into it and make the effort to socialise. The standard of living is generally higher for British and other 'western' expats than they would expect at home doing the same job.
Rent, groceries, shopping and socialising is very expensive, but petrol is dirt cheap, and it's much cheaper to get help with cleaning, childcare, gardening, car cleaning etc. Also we manage to save more money here than we ever did at home as we don't have things like council tax, DH's extortionate train fares, stupid petrol prices, etc.
And it's quite nice being on a compound in a rented house where if something needs doing you just pick up the phone and it gets done for you. eventually
For the first time in 20 years our weekends are our own again, and we can rest/socialise/go to the beach/sit round the pool then have a barbecue - all the things you dream that life should be about!
And it's great being able to go to Asia on holiday without having to spend a zillion hours on a plane. 
But I would say the two biggest factors to being happy with life in Doha are enjoying the job you came out here to do, (and feeling that you work for a decent company and not a bunch of smooth-tongues, lying shysters, which happens - believe me! ) and being happy with the school place for your children. If you feel at all disillusioned with either of those things then it will be much harder to deal with some of the other crap that takes a bit of getting used to.