Let’s get our definitions straight: A dog vacuum is a vacuum that is used on dogs, and a vacuum dog is a dog that vacuums. This invention, the combination toy dog and vacuum cleaner, combines those two necessary functions:

You see, when grooming a dog, it would be helpful to use a vacuum cleaner to clean up the clipped hair. However, because dogs freak out at the noise from vacuums and learn to associate that noise with the sight of a vacuum, they are kind of not into it. See USP 3,771,192, col. 1, lns 8-14.
The dog vacuum dog hides the vacuum mechanism within a toy dog, which has the advantages of muffling the noise and hiding the appearance of the machine behind a dog-friendly face. The tail acts as an extendable vacuum inlet.
I don’t personally know if dogs are susceptible to body horror. If you put a human mannequin in front of me, flipped a switch so it started a monotonic growl, and then yanked one of its arms off to suck bits of debris off of me, I daresay I’d come down with a case of the howling fantods.