Q. Are you allowed to wash a piece of clothing that you wrap around your dog before Tisha Beav?

A. On question 594 we wrote: Although you may vacuum clean a carpet during the Nine Days, even a Gentile should not wash them. The same applies to curtains (Nitei Gavriel Ben Hametzorim 1: 35: 20, Shoshanas Yisroel 4: 9) Horav Shlomo Miller’s Shlit”a opinion is similar.” (See also question 340)
The Rov’s Shlit”a opinion is that the clothing of an animal is alike, and one should avoid washing it during the Nine Days.

Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit”a