Q. On question 1394 Horav Miller ruled you should not wash a dog’s clothing during the nine days. Can you wash the dog itself?

A. Shulachan Aruch (O.H. 613: 1) permits washing off grime and stains even on Yom Kipur, since only the bathing for pleasure is prohibited. Nitei Gavriel (Ben Hametzarim 2: 70: 10, n. 14- p. 402) maintains that it is therefore permitted bathing a child on Tisha Beav, when he is normally bathed daily. He adds that the adult should wear gloves.
Mishnas Avrohom on Sefer Chasidim (1540: 2, p. 201) assumes as an obvious fact that you can do a tahara on a niftar on Tisha Beav, and the chevra kadisha can also wash themselves afterwards if needed.
Horav Shlomo Miller’s Shlit’a opinion is that you can bathe an animal when needed, even on Tisha Beav, but preferably after chatzos (midday), as tzaar baal chaim (animal suffering or distress) may be involved, if the bathing is overdue. (Adding the fact that many dogs don’t necessarily enjoy a bath given to them).

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