If you go to the British Monarchy website there's a drop-down list of Commonwealth realms.
I'm pretty certain that the realms are listed in the order that they were officially constituted as independent Commonwealth realms, at least according to the historians at Buckingham Palace.
The strange thing is that Canada comes after Australia and New Zealand. This is a bit surprising. Canada became a dominion in 1867 before Australia (1901) and New Zealand (1907). Canada adopted the Statute of Westminster when it was passed in 1931 before Australia (1942) and New Zealand (1947). Canada gained full legal control of its constitution in 1982 after New Zealand (1947) but before Australia (1986).
Does anyone have any theories about how they are determining the official order?
It seems important to me, because it could be the closest we have to an official independence date for each country.
New Zealand lawyer here. I'd argue with your dates a little, particularly your statement that: "Canada gained full legal control of its constitution in 1982 after New Zealand (1947) but before Australia (1986)."
I'd put the date for New Zealand in line with Australia (1986). In that year, the New Zealand Parliament passed the Constitution Act 1986, which was the final crystallisation of New Zealand's formal independence. Of particular note, section 26 of the Constitution Act 1986 effectively "patriated" the mechanisms of the Westminster law, while at the same time stating that Westminster Parliamentary law has no effect in New Zealand any longer.
26 United Kingdom enactments ceasing to have effect as part of the law of New Zealand
(1) As from the commencement of this Act the following enactments of the Parliament of the United Kingdom, namely,—
(a) the New Zealand Constitution Act 1852 (15 and 16 Vict, c 72); and
(b) the Statute of Westminster 1931 (22 Geo V, c 4); and
(c) the New Zealand Constitution (Amendment) Act 1947 (11 Geo VI, c 4),—
shall cease to have effect as part of the law of New Zealand.
(2) The provisions of sections 20, 20A, and 21 of the Acts Interpretation Act 1924 shall apply with respect to the enactments specified in subsection (1) as if they were Acts of the Parliament of New Zealand that had been repealed by that subsection.
(3) Without limiting the provisions of subsection (2), it is hereby declared that the effect of section 11 of the Statute of Westminster 1931 (22 Geo V, c 4) (which section declared that the expression Colony shall not, in any Act of the Parliament of the United Kingdom passed after the commencement of the Statute of Westminster 1931, include a Dominion or any Province or State forming part of a Dominion) shall not be affected by virtue of the Statute of Westminster 1931 ceasing, by virtue of subsection (1), to have effect as part of the law of New Zealand.