I understand your frustration but now is the time to harvest ginger, not plant it. Spring is ginger-planting time and, in Victoria, that's probably late spring when the weather is more consistently warm.

I wasn't able to grow ginger when I lived in Melb. It did sprout but then died out, I assume because of the lack of continuous warmth. I know that others have grown it in Melb so it is possible, but not now. Ask again in spring.

Yes, you must plant in spring, preferably late spring,and pick pieces of rhizome that already have shoots protruding. They should do OK but in Melbourne I expect you would have to replant every year.
Wollemia

Rhizomes that have already sprouted would be ideal because you know that they're viable. Best bet for finding these is at greengrocers--especially Asian ones. Sprouted rhizomes aren't that common, though, but also good and easier to find are those where the smooth ends (without the hard skin) are tinged with green. You should be able to find these--just keep an eye out for them in spring. Stay away from the ones with dried shrivelled ends--they'll just rot in the ground.