Hi .. Just thought I'd pop by and add my experience as you are in a very similar situation to me. I also qualified with a First class BA (Hons) in Early Childhood Studies. As Sammy1 said, you won't be eligible here as you need the extra year - to make up to the 4 yr full time duration expected to enable you to teach here.
The one thing I will say though, after applying to three different Uni's, I found I was not eligible to complete a post-grad. After each Uni explained why, I still couldn't make head nor tail of their explanations. Roughly speaking though, it was something to do with the set up of our degree and the components of the study programme. Each Uni however, would accept me onto their undergraduate programme .... Though this wasn't straightforward either. Two of the Uni's would only give me 2 years worth of credit ... Leaving me with two more years to complete. In the end I signed with USQ as an online student as they were happy to credit me with my 3 years of study..... Leaving me with only the 4th year of study to complete. I have to say they have been great - supportive and very well-run for online students.
I definitely agree with Sammy1 on her point about doing your study here - this will really benefit you in enabling you to familiarise yourself with the different early years curriculums and will be a positive aid to helping you when you seek your first teaching position here. I was originally tempted to do the Graduate Teacher Programme in the UK before I moved - what a waste that would've been, as its not recognised here at all !
One last thing, please bear in mind I'm in QLD and so can only advise on what happens in this state .... This may well not be the case elsewhere in Australia.
Good Luck :wink: