I can't speak for New Zealand, but yes, Australia absolutely saw an economic boom in the post-war period- and one that actually outstripped the U.S. economic boom in sheer rate of increase of GDP. Where in the period between 1950 and 1969, the U.S. grew annually at a rate of 3.9% a year, Australia grew at a rate of 5.5% a year. This was a period of 'full employment', where labour demand chronically exceeded supply, simply because the economy was booming to such an extent.
The solution to these chronic labour supply issues, according to a bipartisan agreement of Australian politicians of the era, was to import workers from Europe; the majority of these came from Britain, and with a prominent proportion coming from Northern Europe and then Southern Europe (resulting in the large Greek and Italian communities in Melbourne and Sydney). 2.4 million immigrants arrived in Australia in the 1950-1970 period - a large amount of people considering that the population of Australia in 1950 was about 8 million. During this period, despite the addition of such an enormous amount of immigrants to the workforce, the average level of unemployment was two per cent (which in economic terms is close enough to zero to mean that there was very little long-term unemployment).
So yes, the post-WWII era was a golden era, economically.
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