I think Nike007 has covered it pretty well so I don't have much to add, but as someone who didn't realize she was autistic until adulthood, I think early diagnosis and help can be very important. Your daughter does sound a lot like me when I was a kid, though my sensory issues weren't that severe. I understand your husband's hesitation, and of course it's ultimately up to you both, but risking the label is worth it if it will help keep her from struggling more later on in life.
Good luck with everyone.