I don‘t know for sure (my OpsO mentioned this to me), but I‘ve heard that the trade was full a couple of years ago and that they were trying to cut back.
However, with so many people leaving the CF, I believe that all trades, even MP, are fairly wide open.
The best advice I can give is for you to talk to a recruiter about it.
If you want more information, do a www. search for military police. There‘s also a CDN Military Police Association website that has some (not much, but some) recruiting info on it. It may also be a good place to get some email contacts.
I would definitely urge you to take courses in psychology, criminology, and police investigations. You‘ll find that community colleges will offer more hands-on skill oriented courses in police investigations, etc whereas university courses will provide skills in thinking/analysis of crime prevention and crime related issues such as deviant behaviour, criminal justice system, etc.
I mix of both would likely be good.
Important: talk to people who do the job. They know what it‘s all about.
Hint: the CFRC recruiters can only tell you what they are looking for and how to apply, etc.