It is not a good comparison.
First of all, there is no agreement between the two nations for Australia to defend the air space of New Zealand.
Second, New Zealand is alone, in the middle of nowhere (and not at the centre of the action - they are not really "middle-earth") with minimum 1000 km of water from its nearest neighbour - which happens to be Australia. It does not stand astride any air routes (save when you are actually going there) and in particular, does not stand astride any area that would be considered an air vector of advance for anyone trying to attack Australia (no one is coming over Antartica).
New Zealand is not a threat to Australia, and vice versa. With little in terms of natural resources (unless you are into sheep farming) that would attract invaders attention, thousands and thousands of Km of water protecting it, an Army with tactical transport and naval surveillance assets in sufficient number, New Zealand has enough to discourage any one who would be stupid enough to try something. As a result, Australia doesn't bother, nor does Australia keep any air assets - air or ground surveillance (radars - early warning systems, etc.) or fighters in New Zealand.
Canada, on the other hand stands astride all the major air routes to the US, and definitely astride the air vectoring corridors for any attack by likely enemies such as Russia or China.
Any absence of air defence in Canada, relying on the US umbrella would by necessity mean that the US would - without asking permission or negotiating any thing, trust me on that - move in where they see it required for their own protection to install radars, fighter bases and missiles sites. None of these would take into consideration what happens to the Canadian population if and when ...
At that point, we cease to be a sovereign country, and it would not surprise me in such circumstances to hear voices in the US that would raise a higher ruckus than the old battle cry of "Fifty-Four Forty or Fight".
Our independence as a country requires that we acknowledge the security needs of our neighbour to the South and do what is required to either address them or to participate to the extent necessary to ensure that our interests are heard and accommodated to the maximum extent possible. There is no such inter-relationship required between Australia and New Zealand as what happens to N.Z. does not affect the defence posture of Australia.
As for our relationship with the US in defence matter, its basis what very simply stated in two simple reciprocal political undertakings taken shortly before WWII, which encapsulate both the relationship and the mutual interests in the defence of North America:
In 1938, in a speech at Queen's University, F. D. Roosevelt simply stated: "I give to you assurance that the people of the United States will not stand idly by if domination of Canadian soil is threatened ... ", to which Mackenzie King replied a few days later at a speech in Woodbridge, ON: "our obligation as a good friendly neighbour ... is to see that ... our country is made as immune from attack or possible invasion as we can reasonably be expected to make it and that ... enemy forces should not be able to pursue their way, either by land, sea or air to the United States, across Canadian territory".
IMHO, doing anything less for either country would be to abdicate its responsibilities to its own citizenship as these undertakings, in both cases, are in the superior interest of each nation.
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