I think you must have bought the same Tea Tree deodorant as I did, lol. It's useless!
I bought a new one recently called "Harmoni's Kiss Organic Girl" roll on. It comes in a hot pink bottle with some green on the label. It's almost completely organic, and fully vegan. It works well as an antiperspirant, too, unlike the Tea Tree one. A quick look on the Harmoni's Kiss website, and it says their deodorant is available in Woolworths nationwide
I don't mind the tea tree! I use it with a perfume stick from Lush which I absolutely love! There are quite a few options in most any supermarket now that are vegan though
I find that Priceline generally has a better vegan/organic selection too.
It might be worth checking out Lush's deodorants if you have one nearby. They're definitely different as they come in solid and powder forms, but I really like them.