This is one of the strangest flights in terms of airline operations. It's driven by AU government restrictions on QR - if not for that they would never structure it this way.

So, unfortunately unless someone has specific experiences on this exact flight, you probably won't get an answer. I would try calling both airlines and see which one seems to offer the most help. But your best bet is to arrive extra early to get the best shot at the arrangement you want. I'm sure arriving with a baby early isn't ideal; if you are flying with others they could possibly drop in earlier. You could also drop by the airport sooner (even days before) and talk to the agents that run the flight in person; they may be able to help as well