I have a 10yr old DD who is in the process of getting a diagnosis of AS. As a toddler and young child whenever I wondered about her I would be comforted that she was extremely extroverted, made eye contact, had empathy, needed to be out out out in the world (what i now know was sensory seeking). Teachers used to comment she could and would play with anyone, would never have trouble finding someone to play with etc...
But the thing is as she's approaching 11 it is becoming more and more clear that all those things are true BUT she doesn't read cues well, DOESN'T have good social skills, doesn't understand or use tone of voice etc. What looked like "good social skills" at 2yrs - 5/6yrs was that she LOVES company and the other kids were not necessarily more skilled at tone of voice and various other social skills like genuine reciprocal conversation that she's now obviously lacking. She talked to anyone and everyone with confidence... She seemed fabulously social. She also had a particularly ideal group of peers through preschool, k & 1 and amazing social instruction at school in those years.
I wondered about her as a toddler but the ASD checklists I found (boy lists I now know) didn't fit. If someone had told me when she was 5-6 she had social problems I would have thought they were mad. Now she's approaching 11 am I brutally aware that while she's certainly not full classic autistic that she's certainly not normal either.
I so wish I had an IQ test on her from before the wheels fell off at school, I am pretty sure it would have been high. But she had 2.5 increasingly disasterous years at school (academically not socially) before her first IQ test, where her IQ could not be calculated due to spread (WMI 13th and VCI 96th). Two years of remediation later we had a FSIQ of 131, verbal still 96thm NV 99th and WM 80-90th. Three yrs since the first IQ test we have diagnosed: CAPD, ADD, Dyslexia, we are on the way to an AS diagnosis, and I would say she's got mild dyspraxia.
To my mind, for my daughter, the AS diagnosis makes sense and pulls everything together. But I would not have understood if I had looked at my daughter at 6yrs old and been told what you have been told. Despite my disbelief in her case it would have been true. I obviously don't know your daughter and can't tell you how true it is for her. Just saying I appreciate the possible truth of what the psychologist is saying.
AS in gifted girls, particularly if it's mild, particularly if they are extroverts, is very very hard to pin down. But that is my DD.