That stuff is disgusting. It is unecessary (unless there is perhaps some unusual condition) and I woudn't use it. The only vitamin supplement breastfed babies might need is vitamin D. Adequate sunlight exposure with respect to skin tone produces vitamin D naturally, but if your baby doesn't get much sunlight or you have very dark skin you should consider a supplement. Carlson Labs makes an infant vitamin D supplement that only requires a single drop which you can simple put on your nipple before nursing.
If the neonatologist recommended it for a specific reason, then maybe it is warranted. However if it was recommended as something that all breastfed babies need, then it is not needed.
K. Sophia - Mama to my little lactivore, the amazing Mr. X (11/10).