Also the Robot from Lost in Space
, beginning in 1965.
The question is, how far are we extending the definition of "non-human?" It could encompass any anthropomorphic animal characters from early TV cartoons, such as Huckleberry Hound and Yogi Bear. So we need a ruling: is the initial question meant to apply only to science-fictional characters?
And also, here's a character that started off minor, quickly becoming a sort of "breakout character," and one of the best examples of such.
Not exactly minor. Nimoy got second billing in the opening credits from the second pilot onward. However, he wasn't expected to eclipse Shatner in popularity the way he did, let alone attract the huge levels of (mostly female) fan interest that he did.