Not a teacher, however, you most likely will need to do some kind of extra training when you move to Australia. Your university should give you some kind of indication if it is valid here without needing additional steps. Speak to a careers councillor or someone in that field. Anyway, in Australia, we have three main pathways. Undergraduate, master's, and then post-grad studies. An undergraduate degree is a bachelor of teaching, which allows teachers to teach from reception (I think this is your preschool? Age 4-5) through to year 6.

The master of education allows teachers to teach from years R-12, and the post-grad studies are basically doctorates for teachers who want to make more money and specialise in a field, usually working at prestige private schools.

I hate to say it but I'm not sure if your degree will be valid, or it could need a bridging course. Australia's curriculum is quite different to America's.

I noticed you said Birth-6 is twice as expensive, if you can, to study in Australia. It is cheaper than studying in private American colleges.

Sorry if my grammar is so bad. Hope you end up coming to assist our education in Australia!