Is this really so? Quite surprising for a home airport a major carrier.
This is a Melbourne Airport limitation rather than Qantas. They don't have the facilities for offering early baggage check-in beyond the standard 3 hours.
I will be arriving 5:30am and my next international flight is 11:30am. Both flights on QF.
Having a transit more than 3 hrs is okay though, so you should really look into getting your baggage tagged to the final destination while checking in for your first flight, as it means you can proceed straight through immigration and to the lounge.
Qantas can through-check luggage between two separate tickets, especially when it's their own flights.