Insurance for long stay temporary

I'm from overseas and my partner is from New Zealand.
I'm pragnent and we decided to get the baby in Australia and to stay
for the next years here.
How can i get an privat insurance without a medicard.
If it's possible, that the father pais, through his medicard the cost
for the birth? Or has just the mother the costs to pay???
Through who could our child be coverd? Just through the mother or
through the father is well?
What does say the australian familie law to that?

Thanks to everybode, who can help us...

Dani