Unfortunately, you won't be able to adopt the child without the father's consent, regardless of the nature of relationship between you and the mother.
If the father has had minimal involvement in the child's life by his own choice, or has demonstrated a risk of harm to the child, the mother may be able to pursue sole parental responsibility. While this may not give you any parental responsibility, it will limit the father's capacity to have a say about the child's life.
Bear in mind though that this is a very difficult order to have made by the court. The court upholds only the child's rights in proceedings, which is to know, spend time and communicate with both parents and other people relevant to their care (which includes you, her step-father) on a regular basis, insofar as the child's best interests can be met, and it is obliged to make parenting orders that are only in the best interests of the child. It's not often the court will rule it's not in a child's best interests to have a relationship with their father. At a psychological level, not having the influence of a biological parent has often been shown to cause more harm than good.
I want to add that in proceedings, being seen to be unsupportive of a child's relationship with the other parent can often lead to highly unfavourable results. In many cases (and more frequently of late), the court has ordered a change of residency where one parent has refused to acknowledge the importance to the child of having a relationship with the other parent.
Parenting matters are very delicate. There's a lot of right ways and wrong ways to do things, and what a parent decides is right may not be what the court decides is right.
I am sorry if this isn't what you want to hear. I'm a step-parent myself and my step-daughter's mother is a challenging individual, too. It's a difficult situation, but I found the post-separation parenting course offered by Relationships Australia to be very helpful in dealing with the challenges. The court will order it anyway, most likely, so maybe now is a good time to look into it.
Again, sorry if it's not what you want to hear, but I hope I've at least helped in some way.