Travel with Qantas - cannot tell you how glad I am that I did several trips with them - having the bassinette was a godsend, they are sooo helpful, having a proper meal is awesome, plus their headrests are the best of anyone - meaning you get better rest and can be more comfy if you do end up holding bubs.

Seriously, it is worth the money.
And TBH there is VERY little difference between Qantas pricing and JetStar or Virgin pricing (flying WA-MELB anyway) so we now fly Qantas as a matter of routine.

ETA: With Qantas, you will get an infant allowance too - so you can take 2 pieces of luggage like stroller and car seat or portacot for free.