We don't do fluoride here. My understanding is that the benefit of fluoride to the teeth is miniscule--and that is only when applied topically, not ingested. Fluoride displaces iodine, a necessary nutrient, in the body. It also affects the pituatary gland. Ingesting too much can also lead to unsightly white spots on the teeth.
Your pedi may have come highly recommneded, but that doesn't mean that she knows anything about fluoride. In fact, I recall reading here awhile back that the American Pediatric Association (or maybe the American Dental Association) no longer recommended fluoride supplements for kids. You might want to research their official position.