This site claims that the word came into usage in the 1960s. If it did, it caught on fast. I recall it in common usage among kids by 1965.
Also, is there a name for this kind of word that has something of the sense of onomatopoeia, but is not referring to a sound? It just seems to me to be a very good description of someone or thing even if you didn’t know it’s meaning.
There was a recent thread in which someone showed the result when Google Ngram was applied to the phrase “the whole nine yards.” I decided try it for “dumbshit” and “dipshit.” I didn’t bother with “dipstick,” since that has another meaning that isn’t relevant and which probably accounts for most of the uses of the word. Here’s the results: