Great thinking Want2ttc!
Sounds like you have taken a step back and have broken it all down into smaller more manageable pieces.
She should also be eligible for parenting payments now, and along with that, the ability to take out small Centerlink loans (up to $500 I think?) which could be an option when unexpected bills pop up.
I think having the vast majority of expenses dealt with by you and your wife will take a huge burden off her, and she will be able to focus on her new baby.
Even if things pop up (and they will), it will be easier to deal with, having both your emotional and financial support.
Well done. It sounds like a good solid outcome for the moment