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, 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). The process for getting and ATT was simplified by legislative changes in 2015. For details see this RCMP info bulletin.
Certain individuals who need restricted firearms for protection against predators in the wilderness (eg. trappers, prospectors), or for survival (eg. bush pilots), may obtain such a permit through the CFC, after completing a special wilderness handgun safety course.
While self-defence is a legal purpose recognized in the criminal code, it is virtually impossible for an average citizen to get a permit to carry a concealed handgun for self-protection.