Kelvin what do you expect on a flight that takes most of a day from the extremes of the planet. However you cut it one end is going to be as you put it stupid o’clock !
Heathrow has arround 16 to 18 flights land every day before 6 am .
They have enough handlers at least one runway available 24/7 controllers and ancillaries workers that start at 4am each day.
It not an issue !
Though imho this particular flight is pretty much close to the publicity stunt as it gets and effectively takes out capicity with a relatively marginal time saving from Melbourne to boot .
Still Qantas say they have turned round their economical fortunes particularly domestically so back to losses on a marginal Long haul then I suppose.
Oh and more low yield but far more numerous cattle class handed directly via the desert