Andrew Coyne points his readers to a discussion of the Governor General's reserve powers at ThePolitic.com. The powers most relevant to the current crisis are as follows:
“power to dismiss a prime minister who attempts to govern without the confidence of the House of Commons.” This power prevents a PM from clinging to office when under the rules of responsible government he must resign or ask for elections.
power to dissolve parliament and call elections. “This is another case where Governors General normally follow whatever advice is given them by their prime minister. Yet there have been occasions when the GG has refused such advice. In 1926, PM Mackenzie King, realizing that his minority government was about ot be defeated on a motion censuring the government for corruption [does anything change? -ed.], asked the Governor General, Lord Byng, to dissolve parliament and call new elections. Byng refused, and instead called upon Arthur Meighen, the Conservative leader, to form a new ministry” [Patrick Malcomson and Richard Myers, The Canadian Regime, pp. 113-114].
Clearly the Governor General could act, if she deemed it constitutionally necessary to do so. But my admittedly fallible prediction is that she will not.