It may be an obsolete part of the Constitution, but the Queen can remove the Royal Assent given by the GG within a year. There have been some laws given Royal Assent by the Queen personally, which the GG cannot override. I'd like to consider two situations. In both cases the Parliament has approved a bill and the Queen is in Australia. 
 First case: the bill is given Royal Assent by the GG but is repugnant to the Queen. The Queen can bring the law to an end. The GG is powerless to do anything else. 
 Second case: the GG finds the bill repugnant and refuses to give it Royal Assent. The Queen has no issue signing the bill, so she gives it Royal Assent. The GG can't override the Queen. 
 In both cases the Queen has more power than the GG. Wouldn't that make her Australia's HoS?