1. It has nothing to do with how long your daughter has been in Melbourne. When it comes to children's matters, the law is not concerned about the mother or the father. The court and the law are concerned about the child and the child having access and contact to both parents.
So when the court looks at these matters, when a parent wishes to leave and go to another jurisdiction they are concerned about what contact the child will have with the other parent who is left behind.
It is understandable your daughter is in distress never having lived anywhere else but Sydney, but the issue the court needs to determine is what is in the best interests of that child.
2. If the court makes an order that the child be returned immediately to Melbourne, then the authorities in New South Wales will be directed to take the child and return the child to Melbourne. If the child is breastfeeding, depending on how quickly the order is made, it may be that the child will have to be changed to bottle feeding.
I cannot save it will happen but it is a possibility. You should not assume because the child is breastfeeding that the court will not make the order.
If your daughter is also suffering from depression this will be used against her in the application.
3. This will go against the father as he cannot care for the child full-time but the mother can.
4. The child is very young but in order for her to ensure that the child is not directed to come back to Melbourne she would have to propose a plan whereas the child gets older regular contact and time with his father takes place.
5. If she is undergoing medical treatment for any post label depression then she should also continue that the New South Wales when she moves up.
6. If she applies for a relocation order I believe it will be much harder on her because she has to remain in Melbourne whilst That application was heard. As I mentioned earlier it is the consideration of the child spending time with both parents that is the primary objective of the family law.
7. If she's prepared to fight him, then my suggestion would be exactly what you told her to do. She should pack up and bring her child to Sydney and leave him to decide whether he wishes to take her to court.
She must be prepared to then fight him on his application and she may be entitled to legal aid because she is not employed.
I would not suggest that she make an application in Melbourne to relocate to New South Wales because it will be a much harder fight.
The court is more reluctant to make relocation orders than any other.
The following link is what the court says about relocation orders.
Is there anything else I can assist you with?