If you check on the first definition of Colin on this site, you will find that Cailean has been used as a Gaelic form of Columba in Scotland. Columba is the name which originally meant "dove"; the "peaceful" part would be someone's elaboration based on doves traditionally being symbols of peace, but is not really part of the original meaning.
The actual Gaelic meaning of Cailean was "whelp." A whelp is a young dog or wolf. Obviously the interpretation "young child" comes from someone's reasonable idea that the term was originally being used metaphorically to refer to a young child, just as the modern English word "kid" was originally the name for a young goat but has also been extended to human children. But the literal meaning of Cailean would be "young dog", not "young child."