The doormouse was an AI that appeared in the 'Wonderland' setting of Drake's machine. It is based off the similar character who appears in Lewis Carroll's Alice's Adventures on Wonderland.
When Hailey and Neku assaulted the machine, Hailey first encountered the doormouse, March Hare, and Mad Hatter having a tea party. The three AI became hostile, but were destroyed by Neku. (Disruptive Selection)