As a Kiwi without permanent residency, do I have to pay for my childrens' school fees at state secondary school?

Kiwis are treated the same as Australian citizens when it comes to school fees, so you don't have to pay international fees or anything. There are of course a few costs that all parents have to pay, just as in NZ (e.g. admin expenses etc), but that's it. If you Google the Australian state you are living in + schools, you should be able to find the government schools website for that state which will give you full information. e.g. http://education.qld.gov.au/directory/schools/index.html and http://www.education.vic.gov.au/findaservice/Home.aspx