If the GG sends the Queen letters informing her, then Her Majesty will get them in her famous "red boxes" in the morning.
No, I don't think she was "awoken at a painfully early hour." Firstly, because the final results came here at around 1:00PM. Hence, in London the time is 6:00AM (she gets up at around 5:30AM).
By the way, loyal Governors-General tend to send Her Majesty weekly briefs for her red boxes(they are not required to do so).