If walking off your jet lag with a 2 hour hike between terminals doesn't appeal to you, shuttle buses depart hourly between 3:30AM and 2AM from in front of the terminal. Look for the orange and grey Connect bus parked on the curb outside the door. Though these transfer buses are very convenient, they're not particularly friendly. The service is available only for passengers transferring to flights on the same day. You must show your itinerary before boarding the bus. No itinerary , no ride. Qantas, One World or Qantas code share passengers may get complimentary transfer voucher from the Qantas Ticketing Counter for a free ride. Everyone else must pay the hefty $8 fare to the driver.
A taxi between the terminals will still cost at least $20.