You can check in online with your booking reference number. If you want to pick your seat on the domestic leg, you will have do it via Qantas even if it is a BA itinerary, and might be under a different Booking Reference.

At CBR, I would still go to the check-in desk (at Melbourne there is a desk for international transfers) to make sure they will tag your bags right along with all the boarding passes, and (if you have status) give you Express pass for security at Sydney in case it is busy.