I'm not sure what your legal question is here, but I'm going to give my insight based on what I see to be the issue. This isn't legal advice, just my view.
First, the court only makes orders that it deems to be in the best interests of the child, and the guidelines it uses for working that out is outlined in section 60CC of the Family Law Act 1975. Western Australia hasn't referred to the Commonwealth for family law matters, but the principles are the same.
I assume the father initially believed the child to be his? Even if that's not the case and he raised her as his own since birth, the court may recognise him as a father figure and deem it to be in the best interests of the child to continue having a meaningful relationship with him.
A paternity test alone does not remove the father from already having shared parental responsibility if he is recognised on the birth certificate as the father. There is an existing presumption in that case that he is the father, and that cannot be changed unless a declaration of parentage is made by the court.
Even if such a declaration was made, however, the court may still recognise him as a father figure and award shared parental responsibility anyway, especially if the biological father isn't in the picture.
Alternatively, the court might make a declaration of parentage and not give the father shared parental responsibility, but that means the presumption moves instead to the biological father.
Basically, the issue of paternity isn't going to award you sole parental responsibility, and you don't presently have that because the presumption under law is that both parents share in parental responsibility equal unless the presumption is successfully rebutted and orders made for sole parental responsibility by the court.
So, then, the issue of care arrangements.
In family law proceedings, domestic violence orders have very limited effect. First, they're not proof of family violence, only preventative orders to reduce the risk of family violence occurring, and the fact that there is also no corroborating evidence from the police, DHS or another third party is also going to weaken your claim that the child is at risk in the father's care. Even if that were the case, the court will go to great lengths to help the father address those issues long before it will oust him from the child's life.
If I'm honest, as well, only facilitating two supervised hours once a month for two years with no corroborating evidence of abuse other than maybe a comment of a three-year-old is going to look worse for you in family court proceedings than a DVO will look for the father. It shows you're determined to make sure the father's involvement in the child's life is minimised so that a meaningful relationship is impossible to uphold, contrary to the child's needs. The fact that he hasn't paid child support probably isn't going to damn the father either - after all, the child isn't his and you're actions show that you have no wish to involve him as though he is the father, anyway.
You're facing an uphill battle to get sole parental responsibility. It's rarely ordered except in extreme circumstances, and I think you'll find the court will be more supportive of the child having a relationship with him than not.
Just my thoughts.
