My own experience with the Recruiting Centre with regards to Military Police Officer qualifications could be useful. I have a degree in Military History/Political Science and I was told that I could apply, but that the chances of my application going through were VERY slim because it wasn't the preferred degree (Sociology, Psychology, Criminology). The trade is very competitive and my degree would not be considered competitive for that trade.
BUT your best chance is to speak with the recruiter and see what your options are. I decided to officer probably wasn't for me anyway so I am going back to college for Criminology. There is also a program for ROTP Military Police Officer, but it is pretty hard to get, you have to pass the PARE (physical test required by the RCMP), score officer on the CFAT, have experience in the law enforcement field, etc. I had to speak to a PSO to get that information, the recruiter didn't know it existed, I guess.
Essentially it just depends on how bad you want it, there are different options, but your degree would not be considered competitive, and they may not even have any openings in the trade, like I said, talk to a recruiter.