This may be a silly question - but have you actually asked her about testing?
Either asked her for her consent to a test, or asked her for a sample (such as hair sample or a cheek swab)
that you can have tested?
I do not recommend taking samples (eg hair samples) behind her back
or without her consent (such as if you ask for one and she says no).
We have asked her and she said no and that why she said it wasn't his so we don't know what to believe. We need to know what legal action we can take that will help us find out for sure if it is his? The ex has been playing games and we just need to know because if it is his we want to be a part of the child life
Firstly, forget about "...we want...".
This is not about you.
The key driver in all this is the well being of the child.
It's got rather less to do with what the child's father wants,
and has almost nothing to do with what the child's father's current girlfriend wants.
Yes, a child has a right a relationship with both parents.
But that is a right that attaches to the child, not to the parent.
Understand this - a (biological) parent does not have
an automatic right to be "be part of the child's life".
Understand also that that parent's (unrelated, non-custodial) current partner
has pretty much no place in the picture at all.
So, bottom line - even if he is the biological father of the child,
that does not mean that he automatically gets to be "part of the child's life".
However, if he is the biological father, then he still has to pay child support,
even if he never sees or knows the child.
Secondly, the father may be able to make an application to the Supreme Court (not the Family Court)
for a Declaration of Parentage. This process can include a Parentage Testing Order.
The father will need legal advice about how to do that.
In addition to @Tim W's response, I might add that under section 60B of the Family Law Act 1975 (Cth), the child's rights are as follows:
children have the right to know and be cared for by both their parents, regardless of whether their parents are married, separated, have never married or have never lived together; and
children have a right to spend time on a regular basis with, and communicate on a regular basis with, both their parents and other people significant to their care, welfare and development (such as grandparents and other relatives).
So, while your partner may not have a right to be a part of the child's life, the child does have a right to have both parents be a part of theirs - insofar as their best interests can be met. On very rare occasions, it's not in their best interests to have one or the other parent involved, but that is extraordinarily uncommon.
Thus, while a father does not automatically get to be a part of a child's life, determining paternity will certainly extend support to your partner in pursuing avenues that enable him to be a part of the child's life.
There are some limitations to this statement: "Understand also that that parent's (unrelated, non-custodial) current partner has pretty much no place in the picture at all". The 'other relatives' referred to in section 60B of the Act includes step-parents under section 4, which includes those in a de facto relationship with the child's partner, and a 'de facto relationship' is defined under s4AA.
So, if you are in a de facto relationship, you may be in the picture, but the same rule about child's rights apply - it's not about you, it's about the best interests of the child.
Of course, you may not qualify as a de facto partner (yet), in which case Tim W is 100% correct.
I, myself, am a step-parent by de facto and I have no kids of my own, but if I may, I would strongly suggest minimising your involvement in this matter while ever it exists.
Even though this could obviously affect your life in a significant way, it's important that you, as a person who will potentially be concerned with the child's welfare, care and development, also place the child's best interests ahead of your own. That means doing all things necessary to minimise conflict, and in frank terms, that means you staying out of their dispute.
Single mothers - even 'psycho-ex' ones - are owed a certain degree of respect and forgiveness. They are facing significant emotional challenges - the grief of a failed relationship, the outlook of raising a child without the immediate aid of the other parent, the prospect of another woman potentially earning the affections of their child and filling a mother role with no real right to do so.
Stepping on the mother's toes by getting involved is going to exacerbate the conflict, not reduce it, so lend support to your partner, but don't get in the middle of their issue.