Hi K. D -
Speaking as a parent that had similar issues with her child -- don't do it. That is completely irresponsible for the dentist to even suggest putting a young child under to fill a cavity.
My son is high functioning autistic -- so his thresholds for this sort of thing is pretty low. Nevertheless, once we found a really good pediatric dentist -- not just a regular dentist, because they typically have no experience and tolerance for the issues young children have -- everything has been fine.
I won't kid you -- the first appointment or two following his first horrifying experience with the wrong dentist were a little rough -- but now it is no problem at all -- We have an excellent dentist.
Unfortunately, we don't live near you. We live in the L.A. area -- but what I would recommend is ask other parents and ask your pediatrician for some recommendations.
Hope that helps -
J. Z