Since the Forrest has been mentioned I'll throw out some other suggestions.
The Alibi Room in New Farm isn't a veggie place but they do a vegan a mean vegan breakfast "The Combi Driver's Breakfast". It's huge and has bacon, sausages, scrambled tofu, mushrooms, and all kindsa stuff. They also do a Vegan pizza.
YKILLAMOOCOW at the West End Markets on a Saturday morning is a veggie food vendor. I highly recommend the "No Bull Pie" and the vegan "Dagwood Dog". Awesome!
Kuan Yin in the Valley. Veggie asian food place. Does a lot of vegan stuff. I recommend the 3 Combo Meal, which gets you vegan chicken, fish, and pork, with a selection of veggies and rice.
Pu Kwong on Logan Road in Underwood. Veggie Asian food. Some of the best fake meat I've ever eaten. Vegan chicken drumsticks and other delights.
Govinda's Krsna r=cafe on Elizabeth St. in the CBD. All you can eat buffet for $10. On a Monday, Thursday, and Friday, most of the buffet is vegan. Make sure to ask for a "Vegan Buffet" when you go in.
Apparently Kathmandu Newa Chhe'n restaurant in Paddington does a lot of vegan food. I've not been there yet but I'm going there on my birthday (19th September) so I'll let everyone know what I find out.