Get married to your fiance and let her sponsor you for permanent residency. After you get permanent residency, you can apply at the Canadian armed forces. What they say on their website at
http://www.forces.ca/html/index.aspx?m=0&lang=en&sid=162&sm1=4&sm2=0&tab=1&subTab=0Citizens of another country who have landed immigrant (Permanent Resident) status in Canada may also be considered for enrolment when the CF has need of their skill, when the position cannot be filled by a Canadian citizen, and if the national interest would not be prejudiced. However, only under exceptional circumstances will authority be granted to enrol a citizen of another country.
There are no shortcuts to citizenship. You will have to live in Canada as a PR for 3 years before you can apply.