After watching this short-film multiple times and going through various articles and Q/A like this one from Quora and from my own understanding, I deduced that the
short represents Past, Present and Future.
First we see a filthy man in a dirty house searching for a small bug or rodent like thing to kill and he shows signs of Misophonia or Phonophobia. Which looks like a sign of anxiousness and paranoia in the action of the character but the main part comes when we see what that bug is:
It's miniature version of him. And we see that miniature version doing the same thing which the current version will be going to do next:
And then we see that the current version going to face the same fate too:
This whole scenario seems like running behind the past and ignoring the consequences of current actions. Our main character (Present) running behind the Miniaturize-self (Past) ends up crushes by the giant-self (Future).
Also the film name is Doodlebug which itself doesn't have any significance for the story but if we break it, Doodle means:
A figure or design drawn or written absent-mindedly.
Which show the state of our main character who is running after his bugself absent mindedly.