Yes, it will grow! It's already doing it. Lucky you, because supermarket ginger is sometimes treated with a growth-retardant to prevent it from sprouting. My ginger plants came from untreated store-bought ginger. (I'm near Brisbane). Here's the way to do it.

Propagate by root division. Make sure the ginger root you wish to propagate from has not been treated to prevent sprouting. Pieces of root may be placed in a shallow large (about 40 litre capacity) container of potting soil or sand. Ginger prefers a soil with a pH of 6.0-8.0. Make sure the Âeyes are in an upright position when planting. Bury only and 2cm deep. Keep in a warm, sunny position. Water well and keep it moist, but not wet. It will take at least a month to sprout, and the root may be harvested after 5-6 months. After they sprout and form a good root system, they may be transplanted to the garden and spaced 30cm apart. In warmer regions, ginger should be grown in light shade, but in cooler areas it should be grown in full sun. It should be given plenty of water. When grown in containers they should be moved into a cool storage area before frost. Let the tops of the plants dry and turn yellow after which they are trimmed off. They should be watered every month just to keep the roots from drying out. When spring arrives, they can be moved to a sunny, sheltered place to start top growth. In hotter areas, it is best grown in partial shade. More than one plant should be grown so you can have starter roots for the next year's plants. Ginger will not stand the cold, and if over-watered the root will rot. Ginger will seldom flower if grown indoors or in a pot.

Roots may be dug with a spading fork just before frost, or when the pot is full, or the leaves begin to die down. If grown in a pot, the plant should be 8-12 months old before harvesting. To harvest from containers, dump out the roots or feel for them with your hands. Cut off leaf stalks and remove the root, keep as much as required and plant the rest. Store them at room temperature. Ginger root may be grated or sliced for fresh use, or crystallised. They may also be dried and ground. Keep fresh root refrigerated; wrap loosely in paper towel, then plastic. Will keep several months.

What a comprehensive guide to growing ginger. Do you think it would grow in Victoria? I'd love to have a go. I usually buy my ginger from Victoria Market and freeze it. It keeps forever and I find it easy to grate when frozen.
Halina

Any plant will grow anywhere as long as you provide it with the right conditions. In a cold climate, ginger would be happier in a hothouse. It'll be OK in summer, but you can buy mini-hothouses which would suit it over winter. Make one, if you're creative, out of strong clear plastic (which is sold at gardening centres).