I also have a 15 month old daughter and she LOVES V8 juice, especially the low sodium version. She's still a good eater - she still likes her veggies, but she gets excited when she sees the V8 juice. I don't give it to her everyday and I only give her small amounts in a sippy cup. I basically let her decide when she's had enough. She seems to like it and doesn't have much tummy upset from it. If your daughter likes it and shows no symptoms of tummy aches or allergies, I don't see a problem with it. But if you're still worried, you can always talk to her doctor about it. Good luck with the "no veggies" phase.
You can try "hiding" veggies in foods. My mom used to put a little V8 juice in spaghetti sauce when my brother and I were in our picky, "no veggies" phases. (Maybe that's why I love it so much!) There's also a recipe for meatloaf using pureed baby veggies that I saw on the back of a Gerber's cereal box (I think it was oatmeal). Anyway, I haven't tried it yet, but it looks and sounds interesting. It's a hard and frustrating thing to go through, but try to be patient and keep introducing things. She'll like veggies again.