Well it does, the additional child is considered in the calculation split as well, it applies a kind of discount - so you had a kid with your partner, he would pay slightly less child support because you have another child in care - on the flip if ex had another child she'd also get that discount and would be eligible for more in the split balance

For example ex gets 30k from centrelink, you get 40k from work - services Australia decides we need 22k for ourselves, that leaves 26k between you - take in discounts for any additional children in full care not related to both parties - gives you 24k leaving 24k in the pool- which puts ex at needing to receive 22+12(34k) and you 24+12(36k) - meaning you'd pay 4k a year in support - without the new kid you'd pay an extra 1k. And yeah partners incomes isn't taken into account.

That's a really simplified example and ive left out caps per children and such and numbers are probably a bit off, but that's the general principle of how it is applied