Chicken doesn't level? Feeding it does nothing, can't start fighting with it (by itself) if it can't be levelled to start with
Unless this got patched since commenting, it has changed upon unlocking the second pet (200+ levels later)
Lowest I had was level 3, in swamp which I don't understand, and again feeding it had no effect. I remain convinced it was broken, and I now have a lvl 60 pet (as well as 'finding' a lvl 1 enemy - also thought at the time, that it was feeding which would've given pet xp, based on what I was seeing)
It wasn't until unlocking Sterling that feed began to work for example, don't even believe I could change the Pet's fight area before that but unsure