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