What jobs should I be doing in the Australian garden in January?

Watch out for citrus stink bugs and remove by sucking them off with your vacuum cleaner, taking care to avoid the toxic secretions they can squirt at you.
Provide temporary shade for any new or existing plants that are suffering heat/water stress
Plant some carrot seeds
Protect any new plantings from particularly hot days by erecting temporary shade screens
Watch for powdery mildew in roses and other plants. It appears as a film of white powder on the foliage and can be prevented by spraying with a 1:20 dilution of milk in water.
Prune bougainvilleas as hard as is necessary to keep the plant shapely
Deep water, liquid feed and regularly harvest summer vegetables such as tomatoes, capsicums and beans to stimulate extra yield into autumn.
Spread lawn clippings as a mulch about 10cm deep around trees and shrubs to prevent moisture loss.
As the spring growth flush matures on your herb plantings it may be worth considering drying any excess growth that may start to stress out in the heat of summer. Simply place the leaves on some tissue paper or a drying rack and keep in a warm dry spot.