I can probably understand why the plant is called zucchini in the US and courgette in the UK- could be traced to the proximity of the UK to France but how come it's got two different names in Australasia?
Both countries have had plenty of British migrants. However, in New Zealand there's a greater proportion of Scottish (historically politically tied with France) and in Australia it's the Irish. For the latter they weren't the Zucchini eating kind, that only came with migration from continental Europe when the name Zucchini came in.
The name also stuck more with Australian culture with 'Bananas in pyjamas' being supplemented with 'Zucchinis in bikinis'
It's a theory, I suppose, but Australia is - and always has been - more than five times the size of the other country, so far as population goes.
Until the late 1940s Australia had few Italian immigrants, as the population was largely composed of English, Irish and Scottish - just as the other place was. So Australia had a similar mix of people as its much-smaller neighbour, was settled by Europeans (English, Irish and Scottish) much earlier, with a smattering of continental Europeans, including French owing to the significant gold-rushes in the 19th century.
Italians came to Australia in large numbers following WWII and brought their language and cuisine with them, but zucchinis were unheard-of until at least the 70s except by those of Mediterranean heritage. Few went across the Tasman.
The question mentions "Australasia", a term rarely if ever heard in Australia, but common in the other country.
It does not really exist except there and in geography books.