Company housing
Company housing is still available EXCEPT for newhire pilots. Depending on availability, it is either the Pink Villas (in a very desolate area), the Holiday Villas, or the Oryx Rotana Hotel. The latter is the best for new arrivals as it is close to the office and has a store and restaurants in walking distance. The Pink villas might be better if arriving with a family (they are quite large) but I suspect the spouse would be very discouraged by the area.
Company provided transportation stops after the first week. If you are out in the Pink Villas a car is almost a necessity. An option would be to take a month to month rental at some place like the Ezdan Hotel and Suites. Prices from 4500 QAR to 7,500 QAR for studios (the latter has a kitchen, dishwasher, and washer/dryer). It includes internet, local telephone, and twice weekly cleaning and linen change. Walking distance to city centre mall. Good place to park while looking for someplace permanent but probably NOT a good solution if arriving with children.
The people who are responsibly for the housing are aware of the stress they are placing on new arrivals by only providing the first couple of weeks accommodation. Not aware if there is a solution in sight. Best to come prepared with with an idea of some how you want to handle the transition and some exposure to the real estate market through the above websites.