Zardnaar
Legend
I'm a constitutional lawyer in Australia. I don't think NZ constitutional law is very different from Australia's or the UK's (which I also know pretty well) in these respects.
It's not the Queen's job to stop fascist governments. And dissolving parliament other than on the advice of the PM would itself constitute a coup. Some people describe the 1975 crisis in Australia in those terms, but it was a little bit more ambiguous because that government had failed to guarantee supply; but you are positing the Queen dissolving a parliament that has establsihed a government and/or dismissing a PM who enjoys the confidence of a unicameral parliament.
The loyalty of the armed forces to the Governor-General is a device. Given that the GG is herself acting unconstitutionally if she disregards the advice of the PM and Minister of Defence, the armed forces in practice act at the direction of Cabinet. Again, there is no signficant difference in this respect between NZ and Australian practice, and the principle of civilian control over the armed forces, which in practice means direction by the Cabinet, was strongly re-affirmed in a fairly recent High Court case here (the CPCF case, dealing with migrant interdiction).
We never had the 1975 Aussie thing here where the Governor General fired the PM after the opposition leader talked him into it. That one of the powers a GG can use, I think one of the other 3 is she can dissolve parliament. 4 of them have not been used (3 in Aussies case).