I would have thought that your university professors/tutors would be able to give you guidance on the likelihood of your gaining employment as a Primary School teacher without being a native English speaker. I don't know what the general state of affairs is in Australia with primary school teaching, but it should be fairly easy to find out if your level of English would be sufficient. Can the Department of Education (or whatever you have in Australia) not advise you in this regard?
The only thing it's impossible to tell from these threads is the level of your spoken English. Most people write better than they speak, simply because they have the time to think about what they're writing and, of course, their accent doesn't come through in writing.
Student or Learner