I would personally feel comfortable if my Dr. recommended it. If in doubt, there is never anything wrong with getting a second opinion.
I'm deffinately a big supporter of natural remedys, & honestly that is such a small amount that it should be no problem. However, if you are worried about her building a tolerance then you can give her sleepytime tea with honey before bed once a week & that should help her sleep too. Hope everything goes well with your little one.