'Would anybody use "he" or "she" for a rat, a mouse, a goldfish or a louse?'

To the extent that the first three are pets, I think they would be referred to with correct gender if it is known. Wild mice scurrying behind the refrigerator or rats who find their way to the chicken feed are almost always "its." Likewise, a louse is most commonly called an "it," unless it refers to a specimen of the human species, in which case it is also occasionally referred to as an "it" but mostly, in that instance, for emphasis.