Hi J. -
It's good that you are finding out about this now. Your daughter is still so young and it will be easier to change or manipulate her eating habits before she's gotten too set on anything. It's ok that she doesn't like meat, you don't have to have it in your diet to be healthy. Actually meat has a lot of saturated fat already in it, so the fact that she doesn't want to eat it can work in your favor. Cheese does also, so limit it. Lots of fruits, lots of veggies both cooked and fresh, lots of whole grains, oatmeal, and protein in the form of beans or tofu are great. Stay clear of processed foods as much as possible, white bread, fast food, fried food, sugar cereals, and sweets. My daughter still gets some type of sweet per day, but something like a butter cracker (similar to animal crackers), or dates, or dried apricots, or even one small piece of chocolate and that's it. Ice cream is a treat. And like your other poster said, it's doable for sure, you just have to be a stickler with it. Don't buy anything you don't want her to ask for or have. Keep it out of the house. She will not starve herself.
Some tasty recipes can be found at: http://www.chooseveg.com/vegan-recipes.asp
or
http://weelicious.com/index.php
Also, Dr. Joel Fuhrman's book, Diesease-Proof Your Child: Feeding Kids Right will give you a great deal of insight and information along with good recipes too.
There are a lot of wonderful, yummy, tasty things out there to eat that are good for you too, you just have to be willing to try new things and finding sources. It can be a big undertaking, start small and work your way to change. Every bit will help your daughter and family to be healthier! No one's perfect, do as much as you can and allow some not so good eating times to be special occasions. Finding a good balance is key, kids do need fats for sure, just the right ones. Good luck and feel free to email me if you like.