What are the steps to take to request paternity test where the mother refuses to do so?

Want paternity test done, but the mother refuses? Australia location

You will need to go to court to get it done but it can be contested. The courts will consider "best interest of the child" first.

Were you married to the mother? Why are you seeking a paternity test?

Ref:

Legal Paternity Testing in Australia

Australia Court Ordered Paternity Test

Child Custody - Australian Child Custody Laws, Residence of Children Issues & Child Custody with Divorce in Family Law

You can't just request a paternity test. You have to file for custody of the child. Basically you are filing for joint custody with visitation rights. If the mother contests it, then the court will order a paternity test.

How old is the child? More background might help.

Also what is your relationship in the case.