Well, okay. You'll have to forgive me that my knowledge of WW2 (less than some, more than others) doesn't extend to the commemoration of dead pets. That's niche, and as I've said, a weird thing to get obsessed about.
Yes, there was (once) a headstone for a dog.
However, according to a BBC article linked from the Wikipedia page linked from that photo, it was removed in 2020.