There is currently discussion in the UK about the possibility of a future Prime Minister proroguing Parliament in order to prevent it from frustrating their vision of Brexit. A big part of the discussion surrounds whether Her Majesty would accept a request from her Prime Minister to prorogue Parliament, or whether she would send him away and refuse.
A similar situation arose in Canada at the end of 2008, when the then-Prime Minister Stephen Harper was facing a vote of no-confidence in his minority government, which he looked certain to lose. He requested that Parliament be prorogued, and the then-Governor General agreed to this prorogation, thus avoiding this vote of no confidence.
To what extent, if any, would the precedent set by the Canadian Governor General apply to Her Majesty in the UK, or to Governors General in other Commonwealth realms, when their Prime Ministers make similar requests?