Have you discussed this with the man you think is your dad, and would he consent/has he consented?
Are you doing it out of peace of mind/interest just to know because you have doubts, or because you want to bring proceedings in the Family Court?
My understanding is that there must be substantive proceedings before the Family Court for the Court to order someone to take a paternity test. The court will not order parenting testing simply to satisfy the interest or knowledge of a person. The results must have implications for broader questions of parenting or child support.
Section 69W of the Family Law Act 1975 says: "If the parentage of a child is a question in issue in proceedings under this Act, the court may make an order (a parentage testing order ) requiring a parentage testing procedure to be carried out on a person mentioned in subsection (3) for the purpose of obtaining information to assist in determining the parentage of the child."
There are a number of DNA Testing Laboratories/Companies that do both peace of mind tests (for which you'll need his consent - apparently its just a swab of the inside of your cheek) and court ordered tests.