I received a similar offer from qatar university. I do not think it is fake. Why would it be fake? It is not funny, anyway.
Mosti08,
I talked to a guy working at Qatar University as an assistant professor and he said the given benefits are adequate for a family. In fact he told me that most families are just spending a third of that salary and stacking the rest. Then, should you not worry about the amount they have offered.
Another point is being a muslim I feel proximity to the culture but if I were in your shoes I would take a fly to qatar and see the life there and then make the decision since it is an important one affecting you and your family altogether.
Good Luck.