I wrote a reply, but somehow it got lost. So here goes again.
I can't speak to Fiji, but I have been to Australia and New Zealand several times.
The craft center in Christchurch is a must. There are stalls selling handmade costume jewelry, greenstone and wood carvings, and a variety of other items. If the glove stall is still there, look at the selection of winter gloves. I still wear the ones I bought there years ago.
New Zealand jade called Greenstone is made up into very nice jewelry and carvings. You may also see gum from Kauri trees made into jewelry. It looks like yellow amber. Something fairly recent are blue pearls. They are cultured in abalone and pick up the color from the inside of the shells. The shells, called Paua, are used for jewelry and decoration.
I'm allergic to wool, but I found cotton knit sweaters in both Australia and New Zealand.
Other gift items would be lanolin skin creams, tea-tree (manuka) honey, balms and ointments made from emu oil.
Enjoy your trip!