Thank you very much for the fast answers. They are very helpful and I now have all the info I need!
I have already worked out that I cannot use the airside transfer. My next flight is on QR and there is no interlining. I will have no choice but to retrieve my luggage and check it in in T1 again. I am fine with that, as I have a bit over 4h between flights and now knowing T3 should take 30 min or less, means plenty of time in the Qantas FCL :-)