Some commentators have made that proposition, and indeed Mr. King in 1926 immediately resigned upon the Governor General refusing his request. It's not clear to me that the Prime Minister would necessarily be required to resign. It would depend upon the discussion between the Governor General and the Prime Minister at that time.
If the Governor General did not wish there to be an election but there was no alternative government, I could imagine the Governor General, if she refuses the dissolution, asking the Prime Minister, “Do you nevertheless wish to maintain or continue in office?” And he may, at that point, say, “I'm going to resign.” It's not clear, necessarily, that he has to resign.