None. Australia spans three main time zones (AWST UTC+8, ACST UTC+9:30, AEST UTC+10) plus daylight saving variations. Because its territory stretches from the Indian Ocean to the mid-Pacific, it is always daytime somewhere in Australia. No single country is uniformly "one day ahead" of the entire nation.
For a specific Australian city, places like New Zealand (UTC+12/13), Samoa (UTC+13/14), or Kiribati (UTC+14) are ahead by 2–22 hours—but never a clean 24-hour lead for the whole country.