Hi, my brother and sister in law moved to Oz a couple of years ago and we're trying to get over now. Following their advice I am buying, 100% Cotton bedding, summer duvets, pillows, 100% Cotton towels, furniture, plastic food containers, kitchenware. These are all items that cost a fortune in Oz, here you can shop around, I've found great quality at great prices. When a parcel arrives or I come back from shopping with yet more towels my daughter simply refers to me having been 'Oz Nesting'. They also said take everything you can, fill the container to the brim, if you don't need it in Oz you can pass it on, better than ditching it here and possibly regretting it.
Best of luck.