You know what? I don't believe in beating around the bush. When you do that, it can be unclear what you are saying. Personally, I would sit her down and say, "Look, you go around irritating everyone about Veganism, and it is obvious that you don't even know what the term is. VEGANS DON'T EAT EGGS OR DAIRY. Most Vegans avoid leather. If your going to be all "holier than thou", you think that you would find out as much as you can about that which you are preaching. If you don't trust me, just go to veganoutreach.com, and read about egg laying hens and dairy cows."
Then I would cease to be around her. She probably will not change, and all that you can do is change yourself. If she's truly thickheaded, or just plain dumb, she won't change until she figures it out.
Additionally, if you ARE around her, and see her doing the same thing, I would go up to the person to whom she is talking and say, "Sorry, some people don't get their facts straight. Vegans don't eat meat or egss, and, mostly Vegans DON'T try to make everyone they meet feel guilty and defensive. If you are at all interested in helping to alleviate animal suffering, go to vegan outreach.com and check it out."
You won't be popular, but she'll get the point.