'Git' and 'get' - both with a hard 'g' pronunciation as in 'golf' - are just alternative spellings of the same word. To 'beget', in the Authorised Version of the Bible, meant 'to bear a child' and the noun 'get', taken from that, simply meant 'offspring'. It then took on the pejorative meaning of illegitimate offspring...ie the 7-letter 'b' word. Nowadays, it seems to have recovered a little and is usually employed to mean 'idiot', as you suggested. (The word 'brat' meant much the same originally, though it has never gone quite so far downhill.)