It sounds like your daughter is bored. I was considered a "gifted" child. By the time I was in preschool I was reading at a first grade level. I was also musically gifted at a very early age (4 years old). I was not stupid or slow by any means. When I started school, I would constantly drift off, become completely absorbed in my own thoughts, and not hear anything that the teacher was saying. I now think it was because I already understood the material the teacher was covering and I was just plain bored. I actually remember being extremely bored. I have been told more than once that gifted children often become bored in a traditional learning environment, and that they often do not get the best grades, even though they are more than capable of doing the work. They often drift off in class. Some teachers might consider them lazy. At the school that I attended in California, they had what was at that time called the "Mentally Gifted Minors" program. The spring before second grade, I was given an IQ test and a multitude of other tests and was placed in the MGM program. It sounds like your daughter would benefit from a program like MGM, which is now actually called GATE (Gifted and Talented Education). Many schools where I live (in California) offer the GATE Program. I know that in bigger cities, there are special schools for gifted children. I don't know where you live, but it might be worth looking into one of these options for your daughter. I think the psychologist was right on the money. Good luck to you and your daughter.
I agree with Brook as above (my wee lad is gifted) and the psychologist definitely is right. Its actually fairly common for children in the gifted spectrum not to do well academically in school - they get bored with the level of mainstream teaching and just zone out to what is going on around them...get in touch with any gifted childrens support groups or info resources in your area and they can point you in the right direction for help.