As the UK has a Constitutional Monarchy the Queen/King plays no active part in the running of the country (merely offers advice and suggestions to the Prime Minister in a weekly chat)
Dave: Please don't be offended, I intend no disrespect to your system of government and I'm sure that it works well for all UK citizens - but for historic reasons Mrs Windsor (I prefer this name to her official title) also has the same standing in our constitution. However, whilst it might be true that the 94 year old Monarch has taken an advisory role in your country - I'm not sure if this is the same in Australia.
You are probably unaware of our 1975 constitutional crisis in which our Governor General (who is Mrs Windsor's representative in Australia) dismissed our elected PM. The role of Mrs Windsor in this event is still unknown and even after 25 years, Mrs Windsor refuses to release the "Dismissal papers" which would clarify her role in the sacking of a democratically elected Prime Minister.
Again with no disrespect intended, and yes, this is different matter to your reply - I reckon that Australia has grown-up sufficiently - we should be a republic with our own democratically head-of-state!!
Rant over- well almost (see passing reference to our dismissal below)!!
the death of the Monarch has no impact on the governing of the country.
Yes, I understand that your and our Monarchy is the only thing on this planet that is eternal - can anyone explain why someone's DNA is the sole qualifying attribute for the title of head-of-state in Antigua and Barbuda, Australia, the Bahamas, Barbados, Belize, Canada, Grenada, Jamaica, New Zealand, Papua New Guinea, Saint Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Solomon Islands, Tuvalu, and the United Kingdom. - it escapes all logic !
And yes, I'm aware that UK Foreign Secretary (Dominic Raab) is the official deputy for Boris Johnson.
But, my question is what happens if a sitting PM dies under the UK system of government - not what happens if the sitting Monarch dies? If the latter happens, I've no doubt that the universal cry in 16 x Commonwealth realms would be "the Queen is dead - long live the King (Charley-heaven help Australia!!)"!
My understanding (which could be wrong) is no-one knows for sure; there is absolutely no prescribed process for this
As for Mrs Windsor "plays no active part in the running of the country" - would this remain a benign role if the sitting PM dies? Or, if your constitutional crisis in this eventuality becomes the same as our 1975 constitutional crisis - would Mrs Windsor step into the breach and select a replacement? And if so, would this be kosher in your constitution?
Don