Hey there...
You can absolutely teach in Australia... AITSL is only for visa purposes. You just need to get your qualification recognised when you get here, or even start the process now from home. Then you register with teaching council here and you are good to go!
Visa wise, I had no luck with the visa... when I put my case forward, they said they would look at it on an individual basis. However, I was a days out from the TP days requirement... so you never know? It might be worth a try?
Are you over 30 yo?
Best of luck with everything and keep the chin up!
Orlaith