Here are my thoughts:
Whether or not your daughter has an ASD, it sounds like she's not happily adjusted to her situation. What needs to be done to fix things? IOW, are the fixes things which require a diagnosis? Or are they things which will respond to more informal interventions (joining a Brownie troop to make friends, behavioral interventions on either your part or the teacher's vis-a-vis completing tasks, interventions with the other kids concerning social exclusion of peers, etc). What would a diagnosis gain your daughter other than Capital-Letter Interventions like speech, OT and PT?
If there's something to be gained-- and you're the best judge of that, you and your daughter-- then I'd second DeeDee's recommendation (with the addition that I would explain to the autism specialist that the school is trying to push that specific diagnosis and you're not completely on board). If there's not...I'd be telling the school to come up with another plan. Not every difficult social situation is diagnosis-worthy, and in the long run, you know your child far better than they do.
