What about a grazing muzzle, like loosie suggested? :)
I have one on my older girl right now, during the day, and though I feel like a jerk for restricting her grazing like that, I know it's much better for her to have inconvenience grazing-wise than for her to go through the pain of founder. I put it on at about 11am everyday and remove it around 8pm each evening. I've been seeing some real weight loss and that makes me feel so much better.
Your girl is sure a cutie!
Fabio - 13 year old Arabian/Lipizzaner gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.