In the UK, the Royal College of Physicians is a national body/membership organisation that represents doctors - providing examinations, government lobbying, research, professional development training and support, conferences etc.
What would be the equivalent body in your country?
This is blatantly for a project I’m doing 
In Canada, the equivalents would be the various Colleges of Physicians and Surgeons (one in each province; name may vary; link takes you to the Ontario College), and the Canadian Medical Association.
The difference is that the Colleges are regulatory bodies - they don’t represent the doctors, they are the self-governing regulatory body. They set the professional standards for doctors to enter the profession and remain certified, and they respond to allegations of professional misconduct/incompetence. Although they are self-regulating, they do so on behalf of the public.
As such, the Colleges don’t lobby government on behalf of doctors. That’s the function of the Canadian Medical Association, which is a professional association to represent the interests of doctors.
So, a question - is it the case that the Royal College in the UK does government lobbying on behalf of doctors? from the Canadian perspective, that would be a conflict of interest - that’s why in our system there are the two different sets of organizations - one to regulate, and one to represent.
Probably the American Medical Association in the US. This is not a regulatory group; it’s a voluntary membership group that offers the sorts of services mentioned in the OP. (For instance, if a patient had competency concerns about a doctor, he or she would go to their state’s professional licensing board, not the AMA.)
There are also multiple specialty-oriented groups like this, but the AMA is the big generalized one.
In the UK, the regulatory body is the General Medical Council - the Royal College is specifically a doctor’s member organisation
That’s exactly what I was after - thank you Ferret.
Then it would be the Canadian Medical Association that you’re looking for as the representative body in Canada.