I think you should talk to the school's principal. Or whomever is in charge of discipline. Sometimes the vice principal.

I say this because our local public school system has a VERY strict policy on bullying. One of the reasons being past violence, to the point of being fatal, that has occurred in schools.

It doesn't matter that the bullies are 6 years old. In 10 years they will be 16 years old. And 20 years 26 years. Maybe in jail being supported by our tax dollars for committing a crime (an act of bullying) that someone called them on, and stood up to, putting a stop to it.

The school administration would be able to tell you if they have such a program. Thus answering if the teacher/caregiver has been trained or not.

Part of the message from the caregiver was "stand up for yourself", "don't be a victim". Which is a good one, in part. However, when you typically take the law into your own hands in society, you end up in trouble yourself. So obviously your DD did the right thing to begin with.

Hope you find some resolve.