I am unsure why there wasn't earlier immigration from Australia, possibly technological or cultural. Australia is huge, so maybe there wasn't population or resource motivation to explore and settle new lands.
Indigenous Australians were not mariners, they reached australia by island hopping, and at a time when the sea levels were even lowers and thus the distances between islands were lower (Tasmania was a peninsula at the time).
While NZ is close to Australia by air, the Tasman sea is 1700km of open unforgiving ocean. This is not a distance you can reasonably cross as a people with little history of navigation, or even a lot of it. Scandinavia to Iceland is 2/3rds that distance and Iceland was only colonised in the 9th century, by a reasonably maritime culture (mid-era norse).
Indigenous Australians never reached New Caledonia either even though it’s much closer to Australia (~1200km), as far as I know the earliest arrivals were circa 1500~1000BCE at the earliest and from the other side (the Lapita reached New Caledonia from through).
https://en.m.wikipedia.org/wiki/1998_Sydney_to_Hobart_Yacht_...
NZ, Easter Island, and Hawaii are most recent.
They did have boats (dugouts), but they weren’t suited for the ocean.
https://australian.museum/learn/cultures/atsi-collection/cul...
https://en.wikipedia.org/wiki/Ten_Canoes
Also indigenous to the Sahul
* https://en.wikipedia.org/wiki/Torres_Strait_Islanders
who lived on islands and travelled between PNG and Queensland, Australia but didn't venture south past the Great Barrier Reef and to New ZEaland - but did have the boats and seafaring skills.
* https://en.wikipedia.org/wiki/Makassar_people
who lived in (modern) Indonesia but routinely traded and fished between Northern Australia and China
* https://en.wikipedia.org/wiki/Trepanging
again, they never (to current knowledge) travelled around and past the Great Barrier Reef.