There really isn’t a bad time to visit Australia. Given its varying climates and close proximity to the equator, the when all depends on which regions you wish to visit. Obviously, you would not want to visit the “Outback” in February. Picking a time to go can often be dependent on whether you wish to attend one of the many fine festivities such as The Melbourne Cup which is held in November or The Australia Open held in January.
Picking what do to is purely up to you. Australia is as large as the continental US with as many diverse climates and activities to choose from. See iconic landmarks such as the Sydney Opera House, Ayers Rock, or Great Barrier Reef. Choose cultural indigenous experiences, ultimate winery experiences, or luxury experiences. Better yet, don’t choose at all and incorporate a taste of each in your vacation package.