I would. I would talk to a child psychologist or psychiatrist or possibly a developmental pediatrician. It's not just about a diagnosis but also about addressing her needs as she grows and changes. Your insurance company might require a diagnosis in order to pay for services. Also, it will be good to have notes about her now to compare as she grows. I just think it's in her best interest.
Asperger's (when the diagnosis existed - it no longer does) was the diagnosis given to those on the Autism Spectrum who are very high functioning.
It's not exactly easy to know what to do for someone with that diagnosis. You have to recognize the areas where she struggles and see if there is anything you can do to help her - therapy, services at school, etc. Our son has received speech since he was 2 1/2. He had a speech delay, but he's in 2nd grade now and speech is more about social skills and social communication. He's a routine kid. Dealing with changes can be a real challenge for him. He does have sensory issues, and OT has been a great help to him.
Because of the changes in the DSM, Asperger's is no longer a diagnosis. Our son was originally diagnosed with Social Pragmatic Communicative Disorder. We've often been asked if he was on the Autism Spectrum, and his new doctor (old one retired) said she thinks he might be. But time and time again, we've come to realize that it doesn't really matter to us. It might matter to the insurance company, and it might make a difference as to whether or not he qualifies for services. But it's more important to recognize his needs and to do our best to help him.
So your doctor might have thought since you were already addressing her needs, that a formal diagnosis didn't matter. I think it's better to know.