You would not get enough protein from veggies alone. If you balanced it with whole grains, nuts, and legumes then you would likely be okay. Depends totally how your body reacts, and what your body needs.
I enjoy whey, as it is not the same as milk and is safe. It is also full of good amino acids that our bodies and brains are in dire need of.
But if you feel good, and you feel your body is working the way it is supposed to, then maybe you don't need whey.