Yes you are right she is separately titled as the Queen of Canada. That doesn't mean she lives in Canada. Would be nice to have a Monarch that resides here rather than a pseudocelebrity who visits once every few years. 

Really don't understand how having a Foreign Residing Monarch prevents us from becoming like the US. Canadian identity and values really have little to do with the belief that someone can be born into wealth, privilege, and power. Nor do they conform to the notion that our titular figurehead must always be of the same race.