I agree. We really don't have a gun problem in Canada for the most part. The majority of guns used in crimes tend to come from the US, or are stolen. Thankfully, mass shootings are still uncommon up here.
However, the issue with doctors is not just about permits. There is also a big issue at the provincial level. For example, the Ontario College of Physicians and Surgeons of Ontario is the one that regulates who can practice medicine in the province. They have massive hurdles for doctors trying to immigrate. There is no streamlined system to give credentials to medical professionals that might have decades of experience, but worked in Africa or Asia. Fixing that would solve a lot of the issues with our system. But, again, that is a provincial thing, not federal.