XD mirrors, I think she means pets for pets. I can't think of anything else but I know neopets had something like this (and many other sites too I just can't think of any because it's way too late at night and the exact phrase "pet pets" makes me think neopets XD). No, I am not saying anything about it being like neopets, I'm just using it as one of the many examples of what she might mean.
Anyway, on to the actual suggestion. I don't like this idea very much personally. I never liked the thought of pets having their own pets, it's just odd and doesn't happen. They can have friends, but that's entirely different. Humans are the only species (that I can think of off the top of my head) that actually keeps "pets" so having a pet keep pets is just... I dunno.
Anyway, enough ranting, I'd have to say no on this one.