I'm a Canadian, and studied Political Science for 5 years. Technically the Queen, through the GG has great authority in Canada, though not really any legitimacy. The Governor General is appointed by the suggestion of the Prime Minister. So while the office technically has a great deal of power and authority, but because the position is appointed and not elected, there isn't enough recognised legitimacy to allow the GG to do much of significance. Further, because of the King-Byng Affair in 1926, when the GG refused the request of PM King to dissolve parliament and call an election, subsequent GGs have been reluctant to refuse requests of PMs. As I understand it, the King-Byng affair had repercussions outside of Canada throughout the Commonwealth.

The short answer though, is that while a GG could refuse to sign a bill or dissolve the house, they would never do so under reasonable circumstances.

In Australia, there is no “Veto” power as such. The Governor General is required to give assent to all Commonwealth legislation before it passes into law, and it becomes law on his/her granting the royal assent. Under Section 58 of the Constitution, the Governor General

May assent, or withhold assent, to laws passed by Parliament, or reserve laws for the Queen’s assent, or return laws to the parliament recommending amendments.

So what the OP is referring to as a “Veto” would be a withholding of assent. This has not been done by any of the 26 Commonwealth Governor Generals to date, although, for technical reasons, it has occurred in State Government where there is a similar requirement for State Governors to provide the Royal assent.

It is an arguable legal question as to whether a Governor General could go against the advice of his/her ministers in withholding (or granting) Royal assent and there have been theoretical legal arguments on both sides. Ultimately it would be a decision by a Governor General so I’ll give you the words of a past Governor General, Sir Paul Hasluck 1969-74, on the subject.

To give a wholly imaginary and very extreme illustration, let us suppose that at a general election one party received a huge majority in both Houses and immediately (in spite of all objections that might have been raised by their draftsmen or their political opponents and in contempt of a possible appeal to the High Court) put through Parliament a Bill saying that no more elections should be held until the Minister for the Interior decided to hold them. A Governor-General could properly withhold assent to such a Bill on the ground that this was an action that could only be done by Parliament in accordance with the provision of the Constitution for the amendment of the Constitution. Undoubtedly a crisis would be precipitated.

References:

The Australian Constitution

The Office of the Governor General, by Paul Hasluck