The only issues I see would be possible allergies to things in veggie diets such as soy (which is high on the list of allergens). Also, soy in the quanity Americans eat it is not good, there was a Mothering article on soy a few years back, my mother had been telling me that information for years. Another high allergen is gluten, it's becoming more and more. Gluten is in veggie burgers, veggie hotdogs, TVP, breads, soups, etc (wheat, barley, rye and oats).
My ds2 was not able to eat the standard flow of baby food introduction. He was having reactions to bananas, peaches, squash, etc. He had reactions to the grains, rice even. Our pedi was zero help at this point I'd given up on advice from him. I contacted my friend, a LLL leader and she told me to start in on meats. He was almost 8 months old. Meat he tolerated, no allergic reactions or intolerance reactions. So he was bm and meat... After he started eating meat, he started to look a lot better - those are the only photos in infancy that I have where he is plump. And today he eats almost nothing but veggies and fruits, they are his preferrence. At some point I re-introduced the veggies and fruits and he was okay. He never did like or tolerate the grains, never would choose to eat a cookie or biscut (he knew at 9 mo old they were not good for him). And oatmeal forget it! Little did I know then that he was Celiac, he was 3 1/2 when he was dx'd -- so he lived with intolerances to dairy, cracker products etc for a long time. He now can consume raw dairy only without problems, processed dairy will cause him to be ill.
So, I would listen to what your children tell you (non-verbal communication is amazing in infants). Keep an eye out for intolerances &/ or allergies to things that are in higher quanities in veggie diets.
Be sure that as a bfing mom you are getting a good variety of foods in your diet to include the combinations of foods to yeild a complete protein source (if you are into that theory of eating). I personally would introduce meats into their diet sometime after solids are started, but I'm partial to meat b/c it was the only food my ds2 tolerated well for a long time.