There are plenty of sources of protein available for veggies - tofu, quorn, soya mince, eggs, cheese, pulses, lentils etc etc most vegetarian would eat any number of the above every day.
I used to be a veggie but not anymore, just done a red day, its more about limiting your carbs rather than eliminating them. Have you tried cauliflower rice? Everyone is raving about it. As long as each day does contain a good balance of protein, carbs, healthy fats, fruit and vegetables then I don't see why you can't do it?