I agree with all of the above (including about Carlton - I'm afraid all of my reading that'd qualify as peer-reviewed or as-good-as is either work or naval-related at the moment, the last time I read that quality of material about Australian and international politics would have been around 20 years ago - but I may well read more once I've sated my navy fetish, if I'm still kicking

- although I think Carlton did a pretty good job - his attention to detail with naval matters impressed me, so if he was half as rigorous in his aside on the Elias and Gordon case, then it should still be of a similar-enough quality, even if it hasn't been through the formal peer review process (which, in my experience, was hardly a guarantee of quality in any event, although better than nothing)).
However, I'd argue that in 1936 Australia did have a foreign policy in fact, even if it didn't in law. Australia had a state representative in Washington that represented Australia's interests to the US Government. We made statements about our views on Japan's international behaviour (a bit later than 1936, but still pre-Statute). When war broke out, Australia offered the services of the RAN to Britain (rather than just had them assumed) and offered to send troops (and far from all of them). When war was declared, Australia declared war (without any dissent amongst on political side of things, and very little in society more broadly), and if we hadn't, I would consider it incredibly unlikely that Britain would (or could) have forced us to join in. This is the crux of my argument, that Australia (and New Zealand) were the masters of their own destiny. They chose to throw in with the UK, and continue to be part of the Imperial apparatus (which, imo, was a sensible thing for them to do), but it was their choice. Had they chosen otherwise, then it was on them, and it was unlikely Britain would have intervened.
Putting this in the context of a game where one can play as Australia and New Zealand, I would like to see players in charge of those countries having a choice about how they go about things, as I firmly believe those countries had a choice historically. I think one illustration of this is the counterfactual of what would have happened had the ALP not lost the 1931 election, and passed the Statue of Westminster - ie, it was up to Australia, not Britain, what Australia did with its foreign policy. From the time the Statute was passed in British Parliament (and, arguably, from before then to a smaller degree), Australia had de facto control over its foreign policy, even if it generally chose to exercise it in a way that was very much in line with Imperial (ie, British) interests.
This is turning things on its head a bit. I'm saying that to indicate a puppet relationship we need evidence that Britain coerced Australia into taking action against its will. If we make the bar for puppethood being no evidence of asserting policy in defiance of another allied nation then Australia (and Britain, and a bunch of other nations) become puppets during the Korean War, and the US will, at times, be a puppet of the UK during WW2. It also means that Australia doesn't become independent in 1942, it just transfers it's puppetedness (not a proper word

) from the UK to the USA.
I'd argue that the evidence for being a puppet is coercion by the master, rather than defiance by the puppet, as interests need to diverge sufficiently before the kind of defiance you're looking for will be evident but independence can be achieved well before those interests diverge.
I'd also note that Curtin was just another Prime Minister - when he successfully defied Churchill in keeping the 6th and 7th divisions out of Burma, he had no different legal position than Menzies (or Fadden, or Lyons) did before him. The difference was that, by this point, interests had sufficiently diverged to require (in Curtin's eyes, and I personally back his judgement) the need to exercise the independence in foreign policy that had existed for many years before that point.
Australia isn't generally one to debate wars in Parliament before starting them (see Korea, Iraq and Afghanistan), and it's worth noting that declarations of war come in all shapes and sizes (France was covered off in Britain's declaration of war - but that doesn't mean France was a puppet - and at least according to wikipedia (I know, rubbish source, but I'm buggered and doing it quick and dirty - deffo tear it to shreds if wiki's not up to the task) France didn't ratify the legislation that formalised them being at war until the day after Britain had declared war for them). That Australia didn't feel the need for a debate on the matter (which it didn't, there was widespread support for it across politics and society) doesn't indicate subservience, just a unity of purpose and a perceived unity of interest. Australia went "all the way with LBJ" in the 1960s, but (despite perhaps some of the comments by protesters at the time

) we were never a puppet of the US.