116. Commonwealth not to legislate in respect of religion
The Commonwealth shall not make any law for establishing any religion, or for imposing any religious observance, or for prohibiting the free exercise of any religion, and no religious test shall be required as a qualification for any office or public trust under the Commonwealth.
I am not so sure that it would fail on those grounds. The Constitution provides for the free exercise of any religion, but that does not mean that someone can do anything they care to so long as they can hide it behind this provision. Laws in Australia prohibit bigamy and polygamy, and you are not able to rely on section 116 to gain an exemption from those laws. The laws of the land to not allow for human sacrifice, and an appeal to section 116 to gain an exemption would fail as well. Australian Law prohibits the marriage of minors, save with some very limited permission of the court, and you don't get to hide that behind the free exercise of religion either. Female genital mutilation is another practice outlawed in Australia and not allowed to find shelter in section 116.
Be very assured neither the Church nor any other religion has not been given a blank cheque. Section 116 is probably best understood as opposed to any religious discrimination, rather than allowing any practice that might be accepted and endorsed by a religious group.