You are prompted, upon entering the Cove (the robots area) to bring her an ugly sweater.
That makes sense, since Dot is all about fashion. How could someone POSSIBLY wear a sweater as ugly as that? Head over to the Clothes Shop and click on it.
Look, the bot is freaking out! She was right... now all we have to do is complete the puzzle.
After you've wired the circuit, the bot will be completely deactivated and you can get an ugly sweater hand item (everyone) and Dot's robot head (members only).