The fact that the father has to adopt his own child is not irrational. Please note that your son is not married to the girl he impregnated. Thus, their child is illegitimate. When a child is illegitimate, the mother has the sole parental custody and authority and the father only has visitation rights.
If your son adopts his child (provided the mother consents), the mother will relinquish her parental authority and custody in favor of your son. This will make it easy for your son to take the child to Australia. Once your son has already adopted the child, the mother can no longer file for a custody case because she has to execute a written consent to the adoption.
If, on the other hand, your son does not adopt his child, the mother can file for an action to regain custody of the child even if there's a prior child custody agreement because it is the law that grants full/sole parental custody to the mother.
If you need legal assistance, you may send an email to km@kgmlegal.ph
Best regards,
Atty. Katrina