I assume you mean $200 Australian in which case, if it were me, I would definitely book and backtrack to Brisbane, assuming you have the time to do that. Getting between Cairns and Brisbane is fairly cheap and while it would kill some time, that is insanely cheap between Oz and NZ.
Flight to Tokyo: 92,000 yen
Metro to Ginza shopping district: 160 yen
Watching middle-aged Japanese woman dance to U2: priceless