My 6 year old daughter is experiencing a lot of vomiting, diarrhea and a mild fever. At what point should I call her doctor vs treat at home?

Hydrate. Make sure you keep hydrating the child. Fluids by mouth especially water or pedialyte. Don't give gatorade. If child is voiding urine regularly and does not appear sick she should be fine for now. Again keep hydrating your child.
See doctor. If shes vomiting a lot and having lots of diarrhea its time to take her to the doctor. It is very easy for a child to dehydrate so dont hesitate to take her to the doctor.