Wendy, you have a problem that falls under the category of “good problems.” These are a lot easier to cope with than “bad problems.” It does sound as though your daughter is unusually bright, and you will probably continue to have these questions as she ages and goes from one developmental stage and one school to another. Testing is probably not necessary but it might provide you with some helpful guidance. Most loving parents tend to over-estimate their children’s brightness, so test results sometimes just make us mad and defensive. However, if you really feel the need for this, ask your pediatrician or family physician. I am sure there is a facility available in your area.
As for her social behavior, it is every bit as important as her intellectual and academic prowess. In a quality preschool, the staff would take note of your daughter’s unusual talents and arrange a program that provides her with some of the cognitive enrichment she appears to be ready for. They would also note any gaps in her development. For example, it is possible that she prefers 6- to 7- year-olds because she doesn’t get along well with 3- to 4-year-olds. Good early-childhood teachers would immediately recognize that and arrange activities that would be beneficial to your daughter.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.