That is an awesome question and I'm just as puzzled as you are, unfortunately. I've always leaned toward the natural, non-medical, non-pharmaceutical side of things, so if I were in your shoes, I wouldn't give the flouride drops.
Here is an article about the negatives of water fluoridation:
http://en.wikipedia.org/wiki/Opposition_to_water_fluorida...
I've had numerous chats with different people over the years about this subject. One woman who was very against it was mentioning how too much flouride contributed to this certain disease and how this kid from Lakeville, MN had this disease and, go figure, Lakeville has some of the highest levels of water fluoridization in the state of MN, etc.
I've also heard or read somewhere that you can find fluoride occurring naturally in some foods such as cucumbers. Now, I'm not sure if this is because the cucumbers were watered with city water or if it was because they actually contained some natural chemical that's good for our teeth. I would tend to believe the latter, since I believe that pretty much anything we ever need can be found in the plants, minerals and animals of the earth.
I would agree with the person who posted that you should be thankful that you don't have fluoride in your water. If you have well water, you're probably better off anyway because you don't have chlorine and antibiotics in your water. (A natural health practitioner mentioned that we should all take probiotics just because of all the antibiotics in our water supply. Just a side note.)
Questioning your doctor is never a bad thing. Sure, he/she may be an expert, but you can only be an expert in so many things. Doctors are trained to know only certain things which means there are lots of things they don't know. If you're looking for some alternate views, you can check out another doctor with a bit of a different viewpoint: www.mercola.com. Also, there's some interesting news on www.naturalnews.com. Even a simple internet search could at least raise some more questions you could ask your doctor or, if he/she doesn't know, ask someone who would know (e.g. a naturopath).
Awesome question. I hope you find your answer. :)