@GoldSeeker well technically you have to be registered in order to teach or work in any education and care setting here in Australia. If you took diploma in children's services here, I think all you have to do is check in ACECQA's website if recognised yun course and school mo. If you took your ECE degree overseas, then don't apply for student visa anymore, go straight to 189 as long as you have the needed 60points. If approved, only then will you check with ACECQA.
If I were you, take Bachelors in Early childhood teaching, kasi yun sure, you can apply for skilled independent visa or employer sponsored visa. However, it is expensive talaga and that's 3 to 4 yrs of your life. If you do however take Diploma, I think your biggest chance is to be sponsored by an employer in a state where there is a high demand. I am not entirely sure with what the pathway is for diploma. I am just speaking from experience.