The aircraft is a De Haviland Twin-Otter operated by Sun Air (soon to be purchased by Air Pacific, Fiji's international airline). The actual flight would have taken perhaps 40 minutes or so, but this video condenses it to just 2 1/2 minutes. Enjoy.
Here's a brief rundown of the flight. After takeoff they head northeast and out over the Moturiki Channel. At about 1:06 you see the southern tip of Wakaya Island. Next is the east coast of Koro Island. When it gets to about 1 minute 27 seconds, you see Taveuni. The camera then looks out to the left for brief shot of the southwestern tip Vanua Levu and Rainbow Reef (on map below), a popular SCUBA diving area. At 1:46 you get a good bird's eye view of little Korolevu island and the beautiful reefs that suround it. This is where K and I paddled to on kayaks, which I wrote about in the post "Kayak & Snorkel Korolevu - Fiji". In the background is the area of Waiyevo town, all but invisible. Finally, the camera follows the plane's shadow on final aproach over water and beach to a smooth touchdown at Matei.
I hope you get the chance to visit Fiji and fly to Taveuni sometime.