Dr Greg Taylor, senior lecturer in constitutional law at Monash University, writes:

The suggestion, while imaginative, is impractical.

to be arrested you have to commit a criminal offence. Kerr had
committed all sorts of sins against the Constitution, but no criminal
offences. Secondly, the Governor-General may be entirely immune from
arrest anyway, as a reflection of the Queen’s immunity in England.
Earlier in the year, the NSW Administrative Decisions Tribunal decided
on that very basis that it couldn’t compel Professor Marie Bashir,
Governor of NSW, to come along and give evidence to it.

the Governor-General is actually treason under the Commonwealth
Criminal Code, although that particular part of it was not in force

Professor George Williams, constitutional law expert at the University of New South Wales, writes:

There is no provision in the Constitution that would have
enabled the Governor General to be placed under house arrest. In fact,
it would likely have breached Australian law to do so. Placing Kerr
under house arrest could have been unlawful and thereby given rise to
an even larger constitutional crisis, especially if the police refused
to obey the order.

I believe that Kerr was wrong in acting as he
did, but it is an issue about which people still disagree. There could
be little doubt, however, that detaining Kerr would have been unlawful.
Ironically, if Gough Whitlam had acted unlawfully in detaining Kerr
this could have provided a more sound basis for Kerr to act to dismiss
him than the pretext Kerr actually used.

In the circumstances, I
think that Gough Whitlam did the honourable thing by accepting a
decision he believed to be wrong. In doing so, he saved our
institutions of government from even greater damage.

David Flint, national convenor of Australians for Constitutional Monarchy, writes:

When the former Indonesian president General Suharto heard
of the dismissal of Gough Whitlam, he asked our Ambassador Richard
Woolcott why Mr Whitlam just didn’t arrest the Governor-General. It was
the obvious thing to do – to a dictator or potential dictator.

we learn that Paul Keating wanted to do precisely that. The crowd
laughed at what they assumed he was joking. He wasn’t. He said that had
he been Prime Minister, he certainly would have done that.

fact that Mr Whitlam was no longer prime minister and could not order
anything – apart from a steak for lunch – seems to have eluded Mr
Keating. And under our law, including the proposed anti-terrorism law,
a prime minister has no power to detain anyone, as Billy Hughes once
found when an egg was thrown at him and the police refused to arrest
the miscreant.

An order, say, to the Army, to place their
Commander-in-Chief under house arrest would have been ignored, Mr
Keating even leaving himself open to a criminal charge and worse,
public ridicule.