While Qantas in Sydney has all-day international check-in, Melbourne does not, unfortunately. You should be able to drop bags from 3 hrs prior to departure.
Forgot to add. QF 81 Sydney to Singapore on Sat 28/10/23. I dropped bags off at the manual counter at 600am and they had to open the flight, but wasn’t an issue for them. I was nearly 7 hours prior to departure - wanted to spend plenty of time in the Lounge. I think First was the key.