Considering Japanese subs were operating around NZ and in the Cook Straight, and they flew reconnaissance flights over both Wellington, and Auckland the difference in the perceived threat may not be as great as you think, also consider that Japanese activity just next door in Australia (Sydney, and Darwin) would make the threat to New Zealand seem greater.
Certainly the threat was taken seriously by the New Zealand Government. The army changed it's training so new recruits were taught to shot before they were taught to march, Guerilla warfare training was give, and research was carried out into native foods that could be used to feed Guerilla fighters. Airforce recruits waiting for flight training received infantry training and would be used as infantry if the invasion happened before they got to flight training. The 2nd NZ Div in the Middle East didn't receive any reinforcements for IIRC 9-12 months. Old rifles were converted into poor LMG's, bulldozers were converted into crap tanks, and trucks into armoured cars, various other small arms were being produced in small quantities, and one offs for the defense of New Zealand including SMGs and Mortars. Families were hiding food in the bush so they could escape if the Japanese suddenly landed. Demolitions, and road blocks were set up. Apparently the field gun beside the Cambridge Cenotaph was taken away and buried because of concerns that the Japanese would think it was a military target and bomb it, the gun was never recovered.