Wow thank you all for the amazing support!
Very clear and straightforward answers, descriptions and advices, thanks a lot!
While flying got kind of a non-event for me within Europe/ Schengen I still feel like flying for the first time every time when its "international"/ overseas .

I checked back with Expedia and I am booked on one ticket, which makes things easier.
Nonetheless I think I'll try to get all my stuff for the 3 week trip in my carry-on baggage (well 2 weeks is on Fiji - so besides swimming trunks no need for clothes and living as an expat in Tokyo I find my self still in a situation where I do not have that much stuff to pack available) and buy toileteries and stuff in AU and Fiji (destination after Sydney).
Will decide that tomorrow, but in case I go for check-in baggage I know now how to handle and hope woodduck is right and Qantas is able to put me on another flight (for not too much charge).

So thank you all!