This is not the earliest "moonshine," and I don't have the OED handy for

"moonshiner," but it's still helpful (to answer Tom Dalzell's query). It's

from the New Orleans Daily Picayune, 29 May 1887, pg. 4, col. 1:

The "moonshiners" are not boys who shine the moon. They are men who make

whisky and cut up their shines in the mountains when the moon is full.