Hi Mauro,
Instructor housing is mostly either apartments or villas. Apartments are mainly in West Bay near the City Center shopping mall. I think there is an option to take a housing allowance, but honestly you'd be better off with the supplied housing.
Most housing is within about a 20 minute drive of the college but if you're coming out as a single engine flight instructor then the majority of that flight training is carried out at Al Khor airfield which is a good 40 minute drive out of the city.
There can be a number of days where there is no flight training due to visibility requirements here as well. FI's here need 5km minimum vis in order to carry out any instruction (including MEP and IR). These days tend to end up being classroom or simulator sessions to achieve your duty hours.
Driving here is not so bad as it can be in areas like India and most of the rules are pretty much a combination of the UK and America. I've been driving here for a few years now without incident so far (touch wood) but it's not like driving in Western Europe. There's a big mix of different driving cultures and abilities here and if you drive with that in mind it's not so bad. Most accidents here seem to be bumper or panel damage but there are some big ones also.
As for shopping and general living for the family (apart from perhaps the roads) I'd say Doha is about the safest place I've ever been - and that includes my home village back in England. There are no areas of the city that I don't feel completely safe at any time of the day or night and the culture is very family centric.
Hope that helps,
Chinchilla.