The Anti-Loop Hat is a device presumably made by Zim at some point during The Dookie Loop Horror so he would be aware of the fact that he's in a time loop. How or why was it made in the first place wasn't discussed, but presumably it holds some of the same technology that was used to contain the "time poop" and made the time loop possible in the first place. At first the Anti-Loop Hat was beneficial, as Zim knew what to expect and even knew that no matter what he did, GIR would always end up in the "time poop" containment pod.
Ironically, by being aware of the loop thanks to the hat, Zim slowly lost his mind due to having to repeat the same day several times, and is destined to relive the same day as he failed to figure out how undo the time loop.
Interestingly, Zim must have made more than one hat as the scrapbook he was making of all the times he killed Dib was also wearing one, which means that even inanimate objects can be immune to the time loop as long as its wearing the anti-loop hat.