Can't remember if you said her pencil grip is Ok/normal? (tripod grasp). If she is holding a pencil incorrectly it could be she has weak hands/low muscle tone.
I would probably take her in for a private OT eval, specifiy that you are concerned with both fine motor and writing (but esp. writing) and they can do assessments to at least see if there is a fine motor issue. Some OT's can diagnose disorders like dysgraphia and others don't. But all of them can diagnose motor issues.