I am not a parent, but I do like your approach
It might be useful to explore why people do eat meat and dairy. For example, as a woman she will be regularly told to eat dairy to obtain calcium and prevent osteoperosis. You could talk to her about what osteoperosis is, what other factors affect osteoperosis, and what other foods can provide calcium. Is nutritional advice always unbiased? Or is it sponsored by food manufacturing companies?
Perhaps you could involve some other people, like an older family member who lived on rations during the war? Maybe there is a nurse or fitness instructor in your community who has reasons for eating meat or dairy?
Some farms now do open days, so it could be really interesting for your daughter to have a look around a livestock farm. However, they try to look very cute and friendly - you may have to fill her in on the details of how an animal gets from the field to the plate!
One experience that really stuck with me was when my father (a vegetarian) took me to a fish market as a child to see all the dead fish and sea creatures. He never pressured me to be vegetarian (and I didn't become one until I was adult) but would ask questions like "How would you like it if someone came along and carried you off in a net to be eaten?"
