Honestly, I would have a serious problem with a doctor wanting to examine the genitals of my pre-pubescent, non-sexually active child without a definitive reason- not just as part of an exam.
And if my child objected, there would be no way in hell
that I would force her to have the exam.
I think you did the right thing by protecting her.
Realistically, any doctor who is working with young girls should be sensitive to their modesty and feelings (which are usually very strong at this age), and should not
be allowed to use an unwillingness to have their genitals examined as a reason to fire you as a patient.
I would report this doctor, to the office manager, to the insurance, and to the board that directs and oversees his practice.