In Mongoose JTAS issue 4, there are three psionic animals. The Psi-bee is an insect analogue that exhibits a psionic hive mind. The next is the Ship's Cat, which has the ability to comfort emotionally distressed crewmembers and [apparently] teleport past locked doors. Lastly, there is also a Zhodani quadruped named a 'ziavbro' that is psionic with a Psi stat of 12 and Awareness and Telepathy Talent 0. They look like a three-eyed purple Samoyed dog.
In MgJTAS 6 there are also two animals that are emote-ivores. While they don't have psionic statistics, I suggest that gaining nourishment via empathy is a psionic ability of some form. They are 'Sac'se'qan' and the 'Khal'oman'. The sac'se'qan feeds off anger and aggressive behavior and the khol'oman feeds off dreams.