As a mental health professional, I would be concerned that while gifted children can feel lonely and not understood, and show symptoms of anxiety and depression (often expressed as irritability), it sounds like her symptoms might be outside normal limits for just a typical gifted children. I would suggest finding someone who is simply a good fit for your daughter and bringing some brief paperwork on common behaviors seen in gifted children for them. I wouldn't necessarily limit your search to professionals trained with gifted as you might be looking at other causes.
In the meantime, I would also recommend the parenting book "The Whole Brain Child" by Tina Payne Bryson and Daniel Seigel. It would be very helpful in guiding you and your spouse through how to respond to her behavior.
On a sidenote, if you are needing your insurance billed, the clinician will have to have a diagnosis to bill under. You and your spouse may have to have a conversation about getting services that she needs with a potential misdiagnosis, or avoiding a misdiagnosis and maybe not getting the services. Lovely medical model!!:P
