"We would prefer a female, one that is very stern, but also on the nurturing side!"
That sounds like criteria for a nanny, not a doctor. A good psychologist is adaptable to the needs of his/her patient. They should not have one particular manner about them for everyone. If your daughter needs firmness, she will get it. If the doctor doesn't think that is the right thing, she won't. This is not something you get to dictate. Not if you want your daughter to get actual effective help.
The best referrals tend come from other parents in the area. Ask around. If that doesn't get you anywhere, then just pick one. If it isn't a good fit, you can switch.