Clearly something is very, very wrong. Neither you nor, especially, her little daughter should have to put up with the abuse. There must be something very sweet about your girlfriend when she is in a good place for you to have moved in. Before you move out, it’s worth a try to help her be her best self more consistently.
I can’t imagine that your girlfriend likes who she is when she is in the grip of her rages. I hope you can sit down with her in one of the calmer moments and talk with her about seeking some help, if not for her own sake, for her daughter’s. Is she aware of the changes in her behavior? Has she always been like this? Is she willing to accept some help? If so, the place to start is with her primary care physician to make sure there isn’t something physically wrong. If she is medically fine, then she needs to see a psychiatrist for an evaluation and perhaps some medication to help stabilize her moods. In addition, a therapist can help her learn to cope with her feelings without taking them out on the people who love her.
I hope you can hang in for awhile to see if you can be a positive influence and to protect the little girl. If you can’t, please look for another way to make sure the child is taken care of. Is there a grandparent or another relative who can be helpful? They may not be aware of how bad things are for the child. If there is no natural support for this family, please consider getting children’s protective servives involved. As difficult as that may be, children come first. It’s more important to protect the child’s mental and physical well-being than to protect her mother’s feelings. Hopefully, protective services can offer her some support to be a more stable mother.
I wish you well.