Authorizations to Transport Firearms
You do not require a federal permit to transport a non-restricted firearm. It can be moved and kept anywhere in Canada, assuming it is safely transported and stored, as well you must abide by any relevant provincial or municipal regulations. In some provinces you need an authorization to take any firearm out of your residence unless you are going hunting or to a gun club. You need a valid Firearms Licence, and if you have a restricted firearm or live in Quebec, a Registration Card for the firearm, to be in legal possession of a gun.
You do need a permit to transport a restricted firearm, though. These permits are called "Authorizations to Transport" (ATT). There are two basic versions: those issued for a specific point-to-point trip for an acceptable purpose, and those issued for multiple events or for an extended period (eg. to all approved shooting ranges in the province of Ontario for three years).
If you acquire a restricted firearm, move, or take your restricted/prohibited firearm to a gunsmith, gunshop, or gun show, you would get a one-time ATT by calling the Canadian Firearms Centre at 1-800-731-4000.
If you use your firearm for work, or if you belong to a gun club and want to use your restricted firearm for target practice, you would get an ATT valid for an extended period of time (up to 3 years). In some provinces this permit is obtained by and through the organization you belong to - i.e. the gun club, or your employer.
Certain individuals who need restricted firearms for protection against predators in the wilderness (eg. trappers, prospectors), or for survival (eg. bush pilots), can obtain such a permit through the CFC, after completing a special wilderness training course.
While self-defence is a legal purpose, it is virtually impossible for an average citizen to get a permit to carry a concealed firearm for self-protection.