Check medicare for the costs - Medicare Australia.

I didn't think that any benefits were given out (even to PR visas) in the first 2 years but I may be wrong.

I doubt that private insurance would cover this since it's an existing condition. As Anj mentioned use the search facility for previous posts since I can remember this being discussed as well.

If an agent helped you with the visa application it's be worth getting professional advice on this since it could be expensive to have your baby in Oz.

regards,
Karen

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