Hi Srico
A few questions - are you planning on applying for a visa yourself or are you named on a spouse's visa? The reason I'm asking is because I'm a primary teacher and couldnot apply for a 175 visa as the occupation is no longer on the SOL. I'm a dependent on my husband's visa (he's a construction manager).
You would need to check diac but my understanding is that SA is the only state currently willing to sponsor primary teachers at the minute. Or I guess you might be able to find sponsorship of some sort if you are willing to live in a remote/rural area or the outback (but I'm only guessing). If you check the stickies at the top of the page you will find some useful links and look at the diac site to check for up-to-date info.
I do plan to teach in Victoria when (if!) we finally get a visa grant but even then I'm expecting it to be an uphill battle. My understanding is that once you get into a school you can get registered but most schools are reluctant to take a teacher until after they are registered. Tbh I haven't fully researched it - I'll jump that hurdle when it comes.
I honestly hope things work out for you. Try searching this site for a link about teaching in Victoria. You never know what you might find. There are many more people who are vastly more knowledgable than me!