So, the first step your partner needs to take is to contact Relationships Australia or Legal Aid to organise a family dispute resolution conference with the mother. Whichever organisation you contact (my advice is Legal Aid so you can get legal advice as well) will try and contact her on your behalf. If family dispute resolution fails for any reason, the mediator will issue a s60I certificate, which enables your partner to file an initiating application with the Federal Circuit Court of Australia for parenting orders.
The child has a right to know, spend time and communicate with both parents on a regular basis, regardless of the nature of relationship between said parents, and your partner also retains shared parental responsibility for the child until there is a Court order stating otherwise, which means he has shared responsibility for making long-term decisions affecting the child. In short, the child has a right to know his or her father, and the father is currently considered - for lack of a better term - an 'equal parent' to the mother, so there's a very good chance that, if it's deemed in the best interests of the child to do so, a Court will make orders for the child to spend time with dad in order to build a meaningful relationship with him.
What that time will look like is very difficult to predict for infants, particularly if they are breastfed, but as a guide, it's a common outcome for the non-primary attachment figure (usually dad) to spend time with their baby on two or three occasions each week, for about two hours on each occasion.
If family dispute resolution does fail and your partner decides to file an initiating application, please feel free to come back here for more guidance. There's a good chance he will be entitled to representation through Legal Aid, but we can help with understanding legal principles and Court proceedings to some extent.