For some reason, I've been thinking quite a bit about Squirrel Girl today. Primarily, I've been thinking about whether the DC Universe has a character like her. I suppose it might help to define that a bit. I'm going off what I've read of her, which is mostly recent things written by Messers. Slott and Nicieza.
Personality wise, Squirrel Girl seems to be a fairly chipper person, always eager to help others in need, whether it's trying to stop a mugger in Central Park, or stop Maelstrom from destroying all existence. She comes off as a bit naive at times, but she's also very logical and reasonable when it's called for*. She doesn't tend to judge. She's brave, humble, and very much seems to believe that superheroes are supposed to be role models. I was going to say that her cheery disposition reminds me of Ice (which is probably how I started thinking about this), but in other ways, but her belief that heroes should stand for something, and her tendency to give others the benefit of the doubt,l is more reminiscent of Superman.
She has a track record of defeating enemies which vastly outclass her in power (a list that includes Dr. Doom, Thanos, and MODOK), which is very Batman in JLA, but her victories, while apparently canon**, don't get much play outside the fairly limited corner of the Marvel Universe Squirrel Girl tends to operate in. I haven't seen her called in as an instructor in Avengers: The Initiative yet, for example. In that sense, the closest comparison is, um, I don't actually know. DC's so hellbent on making their whole universe tie together these days, I'm not sure there's a part of it that can really exist by itself. I'd suggest Adam Strange, but I know there have been references in, I believe Countdown to Infinite Crisis, as to how Adam Strange defends Rann from all kinds of crazy stuff, by himself, so that would suggest he has a widely known rep. Ambush Bug kind of runs around in his own world, but I get the impression that if he defeats a villain, it's incidental to his trying to, I don't know, get a breakfast burrito or something. Not really the same thing.
Then again, I'm not familiar with all the obscure corners of the DCU, so there's probably someone out there with Squirrel's mixture of exuberance, optimism, and relatively obscure history of massive heroic triumphs.
* See her attempt to reason with Penance in the Deadpool/GLI Summer Fun Spectacular.
** Well, the squirrel insisted the Dr. Doom victory is in continuity, because it was drawn by Steve Ditko.