would Canada still have a Governor-General or would the Queen actually function as Head of State?
I suspect the King/Queen would assume the role of Governor -General directly, ie there may not be a G-G in addition other Royals may do the same in the other dominions. to better co-ordinate the resistance as long as it lasts.
the GG is of state yes, but at that time it was in the capacity of the sovereign's representative. the King/Queen was King/Queen of Canada as well as the UK. the country may not have been called a Kingdom but was as much a CM as the UK.
With the new constitution though I think that may have changed.