The Monarchy of Canada is "separate and legally distinct" to the Monarchy of the United Kingdom.
(sourced from
http://en.wikipedia.org/wiki/Monarchy_of_Canada )
In essence, the 16 Commonwealth nations with the Queen as their head of state are all in Personal Union. Indeed, there's a principle which holds that the sixteen must ALL agree on any change to the succession laws (currently, a switch from male primogeniture to absolute primogeniture is pending Australian ratification only), though of course any given nation is free to say "no, we don't want to be bound to personal union any more".
http://en.wikipedia.org/wiki/Commonwealth_realm
I think that she's actually a monarch in North America, Central America, South America, Europe, Australasia and Oceania. (With the right minor PoDs, like India becoming a Dominion in 1938 and South Africa remaining in Personal Union, you could get the clean sweep.)