The Constitution couldn't be clearer:
Section1. The legislative power of the Commonwealth shall
be vested in a Federal Parliament, which shall consist of the Queen, a Senate,
and a House of Representatives, and which is herein-after called "The
Parliament," or "The Parliament of the Commonwealth. "
Section2. A Governor-General appointed by the Queen
shall be Her Majesty's representative in the Commonwealth, and shall have and
may exercise in the Commonwealth during the Queen's pleasure, but subject to
this Constitution, such powers and functions of the Queen as Her Majesty may be
pleased to assign to him.
Criticising the GG for saying (what she has always said even since before being appointed ) that Australians would decide to become a republic at some point, Minchin says she should just say nothing.
Personally, whether she is our Head of State or not (and she is not), I think it is not only OK, but desirable that she should contribute to public debate. And not just defer to the pollies.