Well I would be very careful about walking. Other than the Corniche, I can't think of any place I would consider walking because of the traffic and the large number of reckless, speeding, red-light jumping drivers. It is a dangerous endeavor for sure. You will need at least one car, maybe two if your wife likes to get out and about. While gas is very inexpensive here, cars are not. Even to rent a VERY small American car here, you will be paying at least 2000 QR per month.

Other considerations: Is the apartment furnished or not? Do you know where in Doha the apartment is located? Do they only pay for your annual leave ticket or does your wife get a ticket as well?