I think it's great that your daughter is interested! You are raising a compassionate child! I've read several articles stating that vegetarians tend to have higher IQ's than their meat eating counterparts too (I don't believe it is because of the vegetarianism, but just that people with higher IQ's more often choose to be vegetarian)
I wouldn't go into the gory details about animal slaughter or anything, but keep it framed more in an "animals are my friends, i don't eat my friends" way.
WRT your headaches.. are you sure you've been eating enough since you went veg? A lot of people don't realize the caloric difference between vegetarian food and meat since you get filled up on low calorie high fiber "bulk" foods faster than calorie dense meat. What are you eating in a day? Have you also cut out caffeine or sugar substitutes? Suddenly stopping those could also cause headaches.