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The definition of vegetarian is that you don't eat animals, vegans are the ones who don't eat eggs or dairy. And who cares what she thinks anyway, at least you're making an effort to save lives which is probably more then can be said for her.
She isn't helping portraying a positive vegetarian/ vegan image. =(
I knew one person who name-called any non-vegetarians as "corpse eaters" to their faces. It didn't go down well, even if everyone else is well-mannered in handling the situation. I spoke to her in private about her actions will do more harm than good, but she wouldn't listen to me saying that since they (the meat-eaters) are in the wrong to begin with and she's merely pointing out their flaws so she has every right. After a few months, she was next to friendless.
I would recommend not to start an argument with her, since it might be her intention. Once she realised that you won't argue with her then she might go and find another target. Some people are just looking to start fights and for me, it's mine to not start one where they just want to prove their superiority or rightness.
I am a vegan, and I don't eat any dairy at all. Of course some vegetarians still eat dairy products.
My advice is just simply ignore them. They don't understand the difference between a vegetarian and vegan.