I have to admit, and I stress that all parties involved are ones I believe to be beyond reproach and, indeed, for that reason, I think the Governor-General will step aside. I don’t know anything about constitutional law but when the father of your grandchild is in Parliament and you have to decide who governs that’s a conflict of interest. I don’t think anyone thinks that being without a Governor-General right now would be good but that may well be the outcome.
This exposes a key flaw in our current system. It is not simply that we have a Constitutional Monarchy but that the monarchy part is determined by the incumbent executive party. If the Governor-General were elected, this isn’t an issue because the people electing her would be the ones holding responsibility for any personal conflicts and their relevance.
Maybe some constitutional law experts can chime in but if a resignation occurs or even a temporary stepping down, then the Queen will likely appoint the longest serving state Governor as Administrator who will then adjudicate this. That would be Professor Marie Bashir of NSW so it looks like we are covered.