Your post intrigued me, so I did some (informal) research.

I would be skeptical of adding butter to your child's diet although it seems (from a quick Google search) that some pediatricians do recommend it for low weight babies. Before completely dismissing this advice, I would encourage you to do some research on your own. What indicator's is the doctor using for this recommendation? Is is just precautionary? Has the doctor taken into account the size of the parents?

The fact that your doctor indicates you are making "skim milk" seems to indicate looking for another pediatrician might be in order? ... the fat content of breast milk does change during the course of a feeding and can even do so throughout the day. However, the average fat content of mature human breast milk is about 4.2 grams / 100 ml - that seems to be fairly consistent.
REFERENCE: http://www.unu.edu/unupress/food/8F174e/8F174E04.htm (I'm not sure I agree with *everything* stated in the article, but it seems fairly well researched and documented.)

Good luck.