From time immemorial–or at least since the rise of pencil and pen and paper–people have been scribbling nonsensical pictures onto the page when they’re thinking. We call it doodling. But apparently we’ve only been calling it that since 1935. I had no idea it was that new a word! I figured it wasn’t old, but I would have guessed a bit older than that!

There’s a fun quote here from a play of the era:

LONGFELLOW: That’s a name we made up back home for people who make
foolish designs on paper when they’re thinking. It’s called doodling.
Almost everybody’s a doodler. Did you ever see a scratch pad in a
telephone booth? People draw the most idiotic pictures when they’re
thinking. Dr. Von Holler, here, could probably think up a long name for
it, because he doodles all the time. [“Mr. Deeds Goes to Town,”
screenplay by Robert Riskin, 1936; based on “Opera Hat,” serialized in
“American Magazine” beginning May 1935, by Clarence Aldington Kelland] 

And yet we see the word (not with the “draw aimlessly” meaning) way before that, right? It’s derived from dawdle, it seems, and has a meaning of “fritter away time.” 
But in the 1600s it meant “a simple fellow.” It was, in fact, a derogatory term thought to have a, um, rather crude connection. Let’s just say it was extracted from “cock-a-doodle-do” as a euphemism for one of the other words in that sound effect… Yeah, see? Crude. So the British really weren’t being nice when they came up with “Yankee Doodle.”
At any rate, when my 1814 heroine has drawn absentmindedly upon paper, “doodle” is not a word I can use to describe it. 😉