Some further questions if I may...
Is the mother at liberty, or is she in immigration detention?
Is she (or has she been) lawfully in Australia all along
(eg a citizen, a permanent resident, or on another class of visa),
or is she (has she been) been here unlawfully
(eg an overstayer, or in breach of her visa conditions)
Are you worried that the father may try and "claim" the baby from overseas?
Does she plan to take the pregnancy to term, or might she end the pregnancy medically?
If she plans to let the pregnancy run it's course, does she plan to surrender the child for adoption in Australia?