Hello, London and welcome in advance! You will be coming at a lovely time of year. Doha is a big city, so expect big city prices with some nice exceptions. Food is about the same as the US/UK unless you go for specialty items. Petrol is much cheaper. Clothes are roughly the same. Gym memberships vary widely and restaurants are all over the map. Hotels and hotel food are very expensive, small ethnic restaurants are not. Schools are very expensive for children. Furniture can be pricey, ask for furnished accommodations. Your employer should start the visa work for your wife, you will be her actual sponsor. Make sure that's all understood before you come. Yes she can find work, if she wishes. Some Western women find that the hourly wage isn't worth the effort.
Mandi