Which islands are you thinking about? I am not sure of any nearby islands that were settled before Aotearoa. The Chathams are perhaps the closest, but they were settled after.

Otherwise, the greatest barrier to the settlement of Aotearoa was crops that could survive in the colder temperatures as the tropical agriculture of Oceania is generally ill-suited to the climate. The crop that enabled a settlement of Aotearoa was the kumara (sweet potato), which can better handle the climate than the yam/taro/breadfruit staples that are more prevalent elsewhere in the Pacific. When exactly the sweet potato became part of the canoe crops of the Eastern Pacific is unknown, but sometime between 800-1200 CE seems like a fair estimate based on the dispersion of the crop.