1839, irregular formation from vegetable (n.) + -arian, as in agrarian, etc. "The general use of the word appears to have been largely due to the formation of the Vegetarian Society in Ramsgate in 1847" [OED]. As an adjective from 1849. An earlier adjective was anti-carnivorous (1828).
veg
Vega
vegan
vegetable
vegetal
vegetarian
vegetarianism
vegetate
vegetation
vegetative
veggie