Here's that quote from the appendices:
"It was said by Gimli that there are few dwarf-women, probably no more than a third of the whole people. They seldom walk abroad except at great need. They are in voice and appearance, and in garb if they must go on a journey, so like to the dwarf-men that the eyes and ears of other peoples cannot tell them apart. This has given rise to the foolish opinion among Men that there are no dwarf-women, and that the Dwarves 'grow out of stone'."
Obviously, if non-Dwarves "cannot tell [male and female dwarves] apart", then the Dwarf women have beards. Q.E.D.
"It was said by Gimli that there are few dwarf-women, probably no more than a third of the whole people. They seldom walk abroad except at great need. They are in voice and appearance, and in garb if they must go on a journey, so like to the dwarf-men that the eyes and ears of other peoples cannot tell them apart. This has given rise to the foolish opinion among Men that there are no dwarf-women, and that the Dwarves 'grow out of stone'."
Obviously, if non-Dwarves "cannot tell [male and female dwarves] apart", then the Dwarf women have beards. Q.E.D.