This is better posted in LWAB, but in the mean time...White rice cereal has nothing in it but starch...brown rice has a small amount of fiber. Either may be fortified with vitamins, I suppose, since they're not particularly valuable in themselves.
There is iron in breastmilk, and it is well-absorbed, so you need not worry unless you have some particular reason you think she is iron deficient. Besides, what did mothers do before the era of force-feeding infants Gerber rice cereal?!?
Our son didn't really eat foods (and get a significant percentage of his calories from them) until 10.5 months. I let him try stuff starting around 6.5 months (a bite of my banana, some pureed plums, etc.), but he wasn't ready until much later. Grabbing for things (food, spoons, objects) is different than intentionally wanting food.
So if your little one is presented with food and enjoys it, I don't think there's anything wrong with some brown rice cereal in moderation, but there's no NEED for it. Also, save money and grind up some brown rice in a coffee grinder, if you have one, rather than buy cereal!