People are vegan for many different reasons. The two most common are (1) environmental reasons and (2) animal welfare/rights reasons. The value or objective behind why someone is vegan is going to drive the answer to whether pet ownership is consistent with veganism in general.

To keep this question objective [and not too philosophical], let's assume that the vegan is not concerned with animal welfare or rights of their pet and that they are vegan for purely environmental reasons. Which pets are consistent with this vegan philosophy?

The issue is that buying food for carnivorous animals, is inherently not vegan (purchasing animal products), which also have a high environmental impact. So presumably all carnivorous animals are out, but what about herbivorous animals such as rabbits, mice etc.?