There is a cleansing period when you switch to a plant-based diet. Hair fall can occur because of cleansing. However, it will be replaced with new hair if you make sure that your food is organic, that you are eating more raw, more nutrient-dense foods like fruits, vegetables, beans and seeds and less of grains (wheat and rice), and having a green smoothie in the morning.
If the hair fall continues, then check for deficiencies of vitamin B12 and D, and supplement if required.