The current rule
New South Wales, Victoria, South Australia, Tasmania and the Australian Capital Territory move forward at 2:00 a.m. local on the first Sunday in October and back at 3:00 a.m. local on the first Sunday in April. Because Australia is in the southern hemisphere, its summer time runs across the turn of the year — the opposite of Europe and North America.
Queensland, Western Australia and the Northern Territory do not
These three do not observe daylight saving at all. Queensland has held two referendums on it and rejected it both times, in 1992 most recently, with opposition concentrated in the tropical north where the seasonal variation in daylight is small enough that the change buys almost nothing. Western Australia has trialled it three times and voted it down each time.
Five time zones for part of the year
Australia normally runs three time zones. For roughly six months a year it effectively runs five, because the states that change split away from those that do not. Between October and April, Brisbane and Sydney are an hour apart despite being on the same standard offset, and Adelaide sits at UTC+10:30 — half an hour from both its neighbours. This is why Australian broadcast schedules quote times in an alphabet soup of AEST, AEDT, ACST and ACDT.