I'm afraid your Brother-in-Law is going to need an Australian attorney to sort this out. This is not a DIY project that can be handled by an internet forum. He should discuss the situation with his CO, who can refer him to the relevant military authorities that assist service personnel with legal matters.

In the meantime, he can still register his child as a US Citizen by filing a Consular Report of Birth Abroad, which will help matters to an extent.