pets, dogs that don't shed, pee or poop preferable!!!

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Just wondering what kind of dog I can get that doesn't shed, isn't big, preferrably doesn't pee or poop, lol. My daughters want a dog so badly but I'm a phobe about pet hair and them using the restroom in my house so we have avoided the subject for many years. I do however wonder if there is something out there that meets my criteria and is still considered a dog, a real dog. Any ideas?