Obtaining guardianship of a minor who has a non-abusive living custodial parent will be VERY difficult if not impossible. Your best hope is to have the mother's agreement that it would be better for the girl to live with you, in which case you may not even need a formal court-ordered guardianship.
A guardianship is required for two things: (1) to consent to medical treatment, and (2) to register the minor in school. If the mother is willing to sign an authorization to allow you to consent to medical treatment, and is willing to (once a year) register her daughter in your school, a guardianship can probably be avoided. If she is not, a guardianship may be impossible to obtain.
Westlake Village, California