Can't really blame that for Australia's secularism (and I agree Australia is a very secular nation now) - a third of our children attend private schools, most of which are religious. We have one of the highest levels of private schooling in the world, private schools, including religious schools, receive some government funding, and in most states religious instruction is allowed even in government schools as long as parents can opt their child out of it.
No, Australia's secularism comes from somewhere other than that.
Perhaps it is in Australia as it is here, that humanism and the social gospel have bled into the “mainstream” Christian churches. Throw in the media and entertainment, and you’ve got an awful lot of trash thrown at children.