Tulip aftercare in Australia
After flowering, clip the dead flower off the stem, and let the foliage die off while maintaining water level. When the foliage has completed drying out, you may see new little bulbs beginning to form, leave these.
Cut the foliage, but leave the roots, and store the bulbs dry and as cool as possible until early autumn. Then plant them in your garden, using a good mix of soil and compost. Thoroughly water them at planting.
When and where to plant (in my zone) after flowering?
Zone 1 - first week of autumn
Zones 2 & 3 - mid to late autumn
Zone 4 - end of autumn/beginning of winter season
Refrigerate tulips bulbs for six to eight weeks before planting in zones 2 through 5, place them in a paper bag away from ripening fruits (the fruits produce ethylene gas, which destroys the flower bud within the bulb).
Tulips grow best in full sun in well-prepared soil with fast drainage. Avoid planting where water collects, or in locations that are prone to late frosts.
You can find your planting zone here: https://www.anbg.gov.au/gardens/research/hort.research/zones.html