The thing is that the labels "cat" and "dog" reflect a choice in most languages to name animals based on species, which manifests in certain physical/behavioral attributes. Children need to learn by observation/teaching and generalization that these are the characteristics they need to use to conform to our chosen labelling/distinction, and that other things such as size/color/speed are irrelevant.

Of course it didn't have to be this way - in a different language animals might be named based on size or abilities/behavior, etc.

So, your daughter wanting to label a cat-sized dog as a cat is just a reflection of her not having aligned her generalization of what you are talking about when you say "cat" vs "dog" with her own.

And once they learn sarcasm, small dogs are cats again :-)