Emma B's Uk experience thus contrasts with the Oz one, where the following two Sections of the Constitution are relevant.

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.

109 Inconsistency of laws
When a law of a State is inconsistent with a law of the Commonwealth, the latter shall prevail, and the former shall, to the extent of the inconsistency, be invalid.

Apart from that, "God" gets only a passing reference in the preamble ("humbly relying on the blessing of Almighty God") and the "SO HELP ME GOD!" of the Oath of allegiance in the Schedule; nonbelievers can make an Affirmation.

Cheers, Rowan