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If your daughter wants to get into showing chickens, a bantam breed might be a good idea. They are easier for kids to handle and show. Some good breeds for showing include Cochins, Silkies, Wyandottes, Old English Game, Australorps, and Plymouth Rocks. Really, any bird can be shown, but some are just better to show than others.
While Dominiques, Rhode Island Reds, and Ameraucanas would make great egg layers and barnyard birds for you, I would probably not suggest them if you are just beginning to show. True, show-quality Dominiques are hard to find (though they are out there), so you may end up with a lesser quality bird that could dissapoint your daughter. Rhode Island Reds are very nice birds. But, you would have to make sure that you bought one from a breeder, not a hatchery. Most hatcheries sell their own version of "Rhode Island Reds". These birds are excellent layers, but have been bred so much for production that they have lost the ideal color and shape of a purebred Rhode Island Red. Be wary with Ameraucanas, too, as if you purchase from a hatchery, you'll likely end up with what are known as "Easter Eggers". Most hatcheries don't sell true blue egg laying, pure colored Ameraucanas; instead, they sell pretty colored egg laying mixed breeds, called Easter Eggers.
I hope this information helps.