As a previous poster outlined, there are two separate processes that you'll need to go through to be eligible to work at a Canadian carrier.
On the licensing side of things, Transport Canada and the FAA have agreements in place regarding the conversion of your FAA license to a TC licence (note the spelling
). You can check out:
https://www.tc.gc.ca/eng/civilaviati...-fore-1812.htm
for general information and:
Advisory Circular (AC) No. 401-001 - Transport Canada
for information regarding an FAA license specifically. Generally speaking, the conversion process is not too onerous, just the fun of dealing with not one, but two regulators.
There are a few different flight schools, such as "Harv's Air" in Manitoba that specifically deal with these types of conversions.
With regard to the immigration issue, this may be harder. My understanding is that it is not quite as easy as simply marrying the girlfriend. You'll have to check out Citizenship and Immigration Canada to get a full understanding.
Citizenship and Immigration Canada
Cheers!