The first thing comes to mind is a pet name for a little kid. That is how I always heard it and when I hear it I think, “Awwww…” So that is what I thought it was.
It turns out that doodlebug has been around the American vernacular for a very long time but came to more prominence during WWII. American soldiers stationed in the UK during the war gave the nickname to the German V1 bombs that were being hurled against the British.
Now you may think that based on the word doodle, or “to play about”, that the name was given based on the sometimes erratic patterns the bombs would take to their targets. But no. See the name doodlebug was also given to a type of mini race car that was popular in the 1930’s. As it turns out the V1 in flight sounded a lot like the straight-through exhaust system of the mini-cars. So the name stuck.