You're one of the lucky few to get employed by QF. With all due respect Withnail, we are a flexible lot. It's in our culture.
A)QRs.7K housing allowance will be sufficient for a decent flat just by being creative. You can share a flat from a fellow countryman, which a lot of 'em do. They cohabit peacefully and happily. Not unless your family consists of a dozen heads. But, sorry to say though, the current situation will not get you a decent flat all by yourselves for 7K, near or far, from QF. For sharing? Maybe you'll get a flat with a view. And if you can be creative a little more and splice this amount, you can even use a portion of it to buy a brand new car which is a necessity here. Really. :)
B) QF is one of the good employers here. You'll be part of an Institution who's thrust is education, and if that's your passion then you should thank your lucky stars!
C) QF is not walking distance to a mall. Hence again, a car would be a must. Besides, taxis are quiet difficult to get. Buses? That's an option. See and decide when you're here.
D) Unless you're an Inuit the winter cold here would not pose a problem. But the cold here is erratic. It sometimes dip lower than 10 deg.. Better bring some winter clothing. Clothing is a bit expensive here. This will last until Feb.

So, welcome to Doha where Landcruiser is as common as the jeepney back home!! Hope you and your family have a nice stay here! :)