Not your area, but call the nearest children's hospital, what you need is a Developmental Pediatrician. They will have one or more on staff, and they can direct you to that office. It may take sometime to get in. You can also make an appointment with a Board Certified Child Psychiatrist for treatment and request that you have a referal to a Neuropsycholgist for evaluation. You will need to supplement this with a speech and langaguge and Occupational therapy evaluation. Doing things this way will be faster, but you will have to trust that you know what ancellary professionals you need that you may be missing, like a developmental optomistris, geneticist, ENT, Audiologist, etc. The Developmental Pediatrician will call in every kind of specialty needed to fully assess your daughter, and give you a comprehensive evaluation report and treatment plan. Child psychiatrists are usually the best way to go for implementation and case management of the plan, but if you go that route from the begininng, you may want to get the Developmental evaluation eventially.
Public schools won't have sepcialistis in apserger on staff but, they do have school phsycholgist who can do the educational portion of a neuropsychological evaluation to determine the educational need for services in a public school setting to make sure that children with disablities have a basic floor of opportunity to access general education. If she is doing fine in the private setting, and you can aford all of her therapy, there is no reason to move her. The reality is, even if you were in a public school setting, all developmental disablilities stradle the medical-educational boundary, and the school is only required to make your child functional in the classroom, so the lions share of the treatment program, and therapies, are the families responsiblity, if they wish to maximize their child's potential.
That is not to say that school services, if well advocated for, are not worth having, but they have limitations that are not widley understood. Many children with asperger do not qualify for IDEA services at all, becasue of their high function, if they are functional in the school setting without services, and many are.
Good luck! Another source for you to find an evaluator and therapists in your area is www.wrightslaw.com in the yellow pages for your state.
M.