A Hercules should average 300 mph, covering a distance of 1200 miles should take 4 hours. The Canterbury's top speed is 19 knots, covering a distance of 1200 miles should take 63 hours at 19 knots. The OPVs top speed is 22 knots, covering a distance of 1200 miles should take 55 hours, the Danish Absalon's top speed is 25 knots, covering a distance of 1200 miles should take 48 hours.
In a natural disaster type of sealift mission, the army would at best load a ship the next day, and embark that evening, we'll speculate at 6 PM. At the MRV's speed of 19 knots it would arrive at its destination 1200 miles away at 9 AM in two and a half days. The OPV would arrive at its destination at 1 AM in a quarter more than two days. The Danish Absalon would arrive at its destination at 6 PM in exactly two days, similar to an Anzac frigate. Even though the other ships arrived earlier than the MRV, they would probably not start operations until daybreak, so there is no gain. For a ship to arrive 24 hours earlier than the MRV, a ship would have to average 31 knots, not many commerical ships achieve this speed. The scenario above maintains that the ships can sustain their top speed for a few days, weather and sea conditions can extend these times.
As I mentioned before, fast ferries can go twice as fast, but at their top speed of 40+ knots their range shortens significantly to 1100 nautical miles. To achieve the range necessary to reach futher distances with the ability to return without refueling, they have to reduce speed significantly, down to around 20 knots.
Most of the army and most civilians in peacetime sleep at night. If a natural disaster happened in the early morning, the army and government could react that day, but that may be moving too fast. On the other hand if the natural disaster happened in the evening hours or at night, the army and government would react the next day.
Its about 1200 to 2500 miles to different South Pacific island nations, its 1900+ miles to Cairns from Auckland, and its 1100+ miles to Fiji. We know the Hercules can travel to Cairns, that's the airport they used to refuel on their journey to Darwin and East Timor. Obviously the Hercules can use Fiji's airport or others in the South Pacific to refuel as well. Therefore, the air force can respond within a day.
The air force can move the emergency supplies swiftly, but when the navy's MRV arrives, the army should be able to start the rebuilding process and with its helicopters reaching out to the smaller communities.