Horse 1428 - The Queen And The Power to Veto

Whitehall papers prepared by Cabinet Office lawyers show that overall at least 39 bills have been subject to the most senior royals' little-known power to consent to or block new laws. They also reveal the power has been used to torpedo proposed legislation relating to decisions about the country going to war.
- The Guardian, 15th Jan 2013
http://www.guardian.co.uk/uk/2013/jan/14/secret-papers-royals-veto-bills?CMP=twt_gu

In response to an article in the Guardian, Mark Colvin asked the question about veto powers that the Queen has with regard Australian legislation. The answer in black and white is yes, she has explicit powers under s.59 of the Constitution of Australia Act 1900 to refuse assent to bills within one year of them passing the parliament. The much broader question of whether she would though is entirely another matter.

Section 59 - Disallowance by the Queen

The Queen may disallow any law within one year from the Governor‑General's assent, and such disallowance on being made known by the Governor‑General by speech or message to each of the Houses of the Parliament, or by Proclamation, shall annul the law from the day when the disallowance is so made known.

http://www.austlii.edu.au/au/legis/cth/consol_act/coaca430/s59.html

In all Westminster Parliaments that I know of, which includes national, state and provincial parliaments across the Commonwealth, the relevant Governors or Governors-General will meet with their respective Premiers or Prime Ministers weekly to discuss the business of the parliament. The thing is that although relevant Governors always seem to carry certain reserve powers, they only really seem to act, if at all, on the advice of their Ministers.
This is important to note in the first instance as it frames the entirety of any discussion that might be had when it comes to what the Queen or her representatives are even likely to veto.

Try as I might, to even find any instances of veto or reserve powers by the Monarch or their representatives is a difficult thing to pinpoint.
The only real pinch points which seem to cause "constitutional crises" are either when parliaments are unable to secure monetary supply (ie failure to pass budgets) or when the power or person of the monarch themselves are called into question. The King-Byng Affair of 1926 in Canada is of particular note because it involved a refusal by The Governor-General, Viscount Byng of Vimy, to dissolve parliament following a loss of confidence in the Canadian House of Commons.

The 1999 veto which this Guardian article speaks of, happens to relate to the removal of reserve powers from the Queen and placing them into the hands of the parliament. Given the fact that within five years, Britain still went to war in Iraq despite the United Nations ruling it illegal, it suddenly made the Queen's refusal to give Royal Assent to the bill look incredibly sensible.
Also when you take into consideration, the MP expenses scandal followed by the Leveson Enquiry into the ethics of the media and the role that politicians played in that, I start to think that the Monarch stands in the role of the one sane person in the system.

The article also deliberately blurs the line as to what a veto actually entails. The Queen in an official capacity has the power to refuse Royal Assent legislation. The truth is that bills which either never escape the parliament, or were withdrawn from the process, aren't really vetoed in any real sense. If a bill is pulled before it passes through the House of Lords, then if there was good enough reason for it to be abandoned, the chances are that it will have already been discussed in the normal course of business between the Queen and her Ministers. It is also worth pointing out that the Queen by virtue of being monarch, actually owns the parliament. They are called Her Majesty's Government and Her Majesty's Loyal Opposition. I wonder if maybe The Guardian has a hidden agenda and in this case is letting republican undertones fester, or trying to ensure they do.

The question of whether or not the Queen would even veto Australian legislation is almost so irrelevant as to be an exercise in futility to even ask it.
Unlike the UK, the Queen's representative in the person of the Governor-General consults with the parliament. She has enough to be going on with, with the running of that country. It would require the Queen to take an active interest in the rumblings of the Parliament of Australia and considering that it is beyond a lot of people in this country to even name who say the Finance Minister is, to expect that of someone 10,000 miles away is absurd. There is also the matter of Canada, New Zealand, the other Commonwealth countries and all the states and provinces with Westminster parliaments which would also vie for attention if such a proposal were to crystallise.

Really the only possible things that I can conceivably think of that the Queen herself would refuse Royal Assent to that came out of the Australian Parliament would be some bill which would affect the reserve powers of the Governor-General, or perhaps something to do with her capacity as head of the Church of England. I don't think that even an act for Australia to become a republic would be refused Royal Assent; it is possible that maybe that might have been the case in 1911 but even when Edward VIII abdicated, I still doubt that George VI who followed him would have refused it; Certainly Elizabeth II would not.

So then:
Can the Queen exercise veto power? Yes and explicity so.
Would she, or indeed any future monarch? Most likely not.