Trust your body and your instincts. Doctors are trained to give the "safest" answer that will get them in the least legal trouble, and don't often take time to actually try and solve the problem with you. If you think there is a legitimate problem, keep researching and asking around until you are satisfied with the answers you get. YOU are the mom, you know what your baby needs better than anyone!
Truthfully, ANYTHING you give your baby other than breastmilk will be inferior, both in quality and in number of beneficial calories. By supplementing with rice (or, dare I say it, formula), you will be filling her up, yes, but not with anything that will stick to her bones and do her the most good! Breastfed babies gain weight differently than formula fed babies, and often Dr.'s fail to recognize/recall this.
There are medicines your doc can prescribe to help boost your supply, as well as many natural supplements (oatmeal worked wonders for me). You could also try nursing her more often (i.e. on demand), letting her nurse each side completely before switching and simply eating/drinking more yourself. One great resource is <http://www.kellymom.com>.
Good luck,
~E.
ETA: pumping between feedings might help increase your supply, but don't trust how much you pump as an accurate gauge of how much milk you are producing. I was only able to pump 2 oz. at a time, and I KNOW my son drank more than that when he nursed!! (he nursed exclusively for 12 months, and then continued nursing part-time with the addition of "real" food until weaning at 18 months. We never used baby food or formula)