B.C.
I'd be concerned about quite a few things with this behavior.
6 is a little young for an eating disorder, but it almost sounds like what she has - bulimia. Throwing up this often is bad for her teeth and esophagus - the stomach acid can eat away at them.
At least she eats breakfast (can you server her scrambled eggs most suppers?) but I'd also be worried about her growth and development and nutritional problems.
I'd be taking her to her doctor and/or a therapist who specializes in eating disorders and see what they have to say about it.