Whether you pursue a neuropsych, or additional testing with your existing psychologist, depends mainly on your level of confidence in the current professional. A competent clinical or school psychologist is perfectly capable of diagnosing dysgraphia, and providing you with practical recommendations for school or home. In some cases, however, especially complex or puzzling ones, a neuropsych may be helpful. It is not, practically speaking, hugely different from the kind of psychoed eval that your existing psych would most likely conduct, as it consists of the same core instruments (if you went to a neuropsych, you would definitely want to bring your existing WISC/WIAT results, so s/he would not inadvertently duplicate/invalidate testing, and so the results could be incorporated into the assessment). You can get equally good evals from different kinds of psychs. It's more contingent on the clinical and diagnostic acumen of the individual professional, than on their nominal specialization.
Honestly, the results you have right now would be sufficient for establishing the need for dysgraphia/LD-in-written-expression services in many of the districts I've worked in. If that's all you need, then you already have it.
If I were pursuing additional evaluation, not only would I want finer definition of the contributors to her dysgraphic presentation, I would also want to know about the memory area, including whether factors that affect attention were involved (ADHD, auditory processing, emotional interference, fatigue/sleep irregularities/allergies/allergy meds/asthma, etc.), and what aspects of memory were affected (short/long-term, visual/verbal, encoding/retrieval/recognition).
You might consider asking your current psych what would be involved in additional evaluation.
Also, don't downplay her intelligence. The level of diversity across her index scores makes the FSIQ a much less comprehensive indicator of her ability. Verbal Comp is a significant strength, in addition to Working Memory being a significant relative weakness.
