In a monarchy, like kings and queens, that means you think you are better than everyone else. In other countries they make the rules and whoever does not follow would get there head cut off. Well, it was like that a long time ago, but if a king or queen practices Christianity and follows Jesus than they will open there eyes and see we are all the same.
No, the monarchy does not violate the separation of church and state, because the monarchy is mostly just a figurehead. The monarchy in Australia is popular, and the queen especially is well-liked among the people. The monarchy is not promoting any kind of particular religion. The monarchy is just a nice popular family and there is no reason not to have it.