I use Lush deodorant powder! It's called 'the greeeench'. I used to sweat alot during my cycling to school and just smell awful when I got to school and since I've used it it's never happened again. All of lush's products and cruelty free and the powder is vegan. The only downside is that I personally don't really like the smell but if you spray on some perfume you don't smell it anymore! Also it's quite expensive but it lasts really long. Hope this helped!
I go on iHerb and buy the "Herban Cowboy" deodorants. They are vegan. If you buy a certain amount on iHerb then there is free shipping. They ship to Australia.