I think encouraging manners (like chewing with your mouth closed, using utensils as much as possible at her age) is fine. However, I would caution you against scrutinizing or negatively obsessing about your daughters eating habits and weight, especially at such a young age (but at any age, really). My mother, who I love more than words can say, did this for my entire life. I have binge eating disorder and my sister has bulimia/binge eating disorder and resents her very much for it. If your daughter chooses to follow a LC way of eating when she is old enough to decide, then it will be her choice. But its not yours. I would encourage you to help her to see that balanced eating can be fun. 6 year olds do not need to be concerned with burning fat instead of carbs for fuel. They need balanced nutrition for growth.

And please be careful of the faces. Children can see and understand body language. When my mom makes those faces (when we eat, when we try on clothes, etc), it still makes me really sad and angry and brings me right back to being 6 years old on a diet with her making faces at me while I was eating. For your daughter's sake, please tread lightly re: this issue.