Its called a rat doxie. I have 2 and they are adorable if I had a pic I'd send it with this answer.
Yes, I have a female Dachshund and Rat Terrier Mix. I call it a Doxie Terrier. The Dachshund has the nickname of "Doxie". Most "Doxie Terriers" come in many colors, shapes, etc. Some are longer and other are shorter. My dog, Xena, is a little shorter than a Dachshund. She has the coloring and pattern of a Miniature Pincher.