I notice you have not bothered to address any of my points. Thank you then for your implicit agreement.
Please elaborate! 
If you insist.
Note that points 1. and 2. have been taken from Halsbury's Laws of Australia.
1. The exercise of religion protected by s. 116 extends only to the performance of acts that are done in the practice of religion.
- Argument: it is a cultural practice and not a religious one.
Assuming the High Court accepts that it is a religious practice:
2. The protection extended by s. 116 concentrates on freedom to believe, but freedom to act in accordance with religious beliefs is not subject to the same constitutional protection. Conduct in which a person engages in giving effect to his or her faith in the supernatural is religious, but that conduct will not be constitutionally protected from laws that do not discriminate against religion generally or against particular religions.
- Argument: a ban on the wearing of the burqa does not discriminate against Islam generally, considering there is legislation providing for certain standards of dress in public (public indecency being the first that comes to mind).
3. The purpose of the legislation may be taken into account in determining whether it is a law prohibiting a religious practice.
Per Latham CJ(at 132) in
[i]Adelaide Company of Jehovah's Witnesses Incorporated v Commonwealth ("Jehovah's Witnesses case")[/i] [1943] HCA 12.
In that case, a law forcibly dissolving a Jehovah's Witnessess group and preventing it from practising by seizing all its assets was ruled to be constitutionally valid, because its purpose was not to prevent the free exercise of the members' religion but rather to protect national security (it was wartime etc., see the AustLII link if you want the facts of the case).
3a. Jehovah's Witnesses also contained a test of proportionality: one's freedom of religion may be limited by "reasonable" or proportionate laws designed to protect a legitimate public interest.
The High Court said something along the lines of:
Taking into consideration the most likely intentions of the original framers of the constitution, it is highly unlikely that they would have considered making laws against polygamy or murder as infringing upon religion (even though some religions practice polygamy or human sacrifice). Those laws would still be regarded as secular laws, even if indirectly their effect was to prevent some religious practices.
It is therefore impossible that "the free exercise of religion" in s.116(c) meant an absolute right.
You may see this test applied again in
[i]Kruger v Commonwealth ("Stolen Generations case")[/i] [1997] HCA 27. It is this case which really diminished the scope of s.116 by further re.
In the Stolen Generations case, the High Court reaffirmed that a law is only constitutionally invalid under s.116 if it has an ostensible purpose of inhibiting religious practice, rather than merely having the effect of doing so.
The purpose test is the current law, although the Court also acknowledged the necessity of a test of proportionality.
While Gaudron J argued that a law could breach s.116 if
one of its purposes was to prohibit religion, she qualified that test with the following:
- The law is not constitutionally invalid if it is necessary to achieve some overriding public purpose or satisfy some social need.
- The law is also not constitutionally invalid if its specific purpose is unconnected with the freedom of religion.
- Argument: it is quite easy to make a case that the purpose of the legislation is 1) for security issues (see numerous news articles about men wearing burqas robbing banks because they were able to hide weapons under the burqa); and 2) for equality issues. Clearly, 1) and 2) are legitimate public interests. 2) is also a social need.
- Equally clearly, 1) and 2) are unconnected with the freedom of religion.
- It may not even be inhibiting any religious practice, assuming the Court accepted the argument that it is rather a cultural practice (and there are plenty of religious scholars who agree that it is a cultural practice and who could be called upon to testify). Not to mention the large number of women who consider themselves Muslim and yet do not wear any sort of covering.
Even if you were trying to argue by Gaudron J's reasoning, and could show that one of the purposes of a law banning the burqa was indeed to prohibit religion, there is still that matter of proportionality - national and state security is surely a sufficient "overriding public purpose" while equality of the sexes is a significant social need.