We're here in England for the past 4 years now and my wife who is a nurse is applying a job in australia.

We have a Land Tax. It is levied by the State governments (not council, not Commonwealth/Federal) based on the value of land that you hold. But there are exemptions - such as for a main residence. There are Council Rates, but they are not really taxes. Just an annual fee for things like garbage collection and the privelage of living in the Council area. It varies from area to area. I don't pay it because I rent. But for the owner it's much much less than what you're paying, and I am in inner city Sydney.