My cousin's DD had a long long phase like this where she lost huge amts of weight and was hospitalised. It was counted as an eating disorder but a fear one cause her twin was anaphylactic to nuts and she was scared she could die from eating. She was 8 when it started and it has been a long road to recovery. I will ask my cousin for tips on what helped, she was having psychiatric help and still is. I know its much more extreme than your DD's but its similar.