No. The only time you would need "proof" of your disability is if you went to court because you were suing an organization for refusing to grant you and your Service Dog access.
The laws in Canada are slow to catch up with the US, and right now there aren't any laws either for or against Service Dogs, other than for Guidedogs for the Blind. This is changing, primarily because of the use of Psychiatric Service Dogs (PSDs) for soldiers afflicted with PTSD. Right now, anyone can train their dog to serve as their Service Dog. That is good. The bad side of it is that many businesses will not honor Service Dogs because there are no laws forcing them to grant access, as there are in the US. I advise my clients to train their dogs, pass the ADI-PACT test, and make use of the badges and vest they earned. If someone refuses access to your PSD, do not give them your business.