It's best to ring the airline for clarification. Get the name of the person you spoke to and make a note of it and the date.

I actually interpret it as no baggage allowance in Australia. So all you can carry is carry-on for yourself and maybe 3 baby items. If you are flying OS you can carry on 10kg for yourself plus your baby items.

I've been known to pack a bit of my own stuff into the carry bag for our hammock