Sorry, I think I had better qualify one thing.
On a single Qantas DOM to INT ticket with an overnight transit in SYD:
Qantas domestic check-in could not print a Boarding Pass for my next day's international flight or through check any luggage.
I have several times rechecked-in the next day at a Qantas T3 Domestic service desk (international transfers) for the T1 departing flight.
I have then received a printed BP from that T3 service desk.
I have then gone though security and caught the free Qantas T3 to T1 transfers bus.
I *think* on at least one occasion I had checked baggage accepted at T3 as well but I'm usually HLO.
So, on reflection, I'm not confident about the checked baggage being accepted at T3. But I suspect that if they can print a BP, they can accept baggage too.
The reason I was initially confident about it was because when I recently did this, we did have checked baggage. Qantas would only check it to SYD. The next day, when about to return to T3, I was at the last minute persuaded by my +1 to get an Uber instead over to T1. I forgot about that bit. But I remember we then got stuck in dreadful traffic.