Strictly from the Big Two, Marvel and DC both have sites that let you read some of their kids' comics for free; if she goes for any of those, you can dig deeper for back-issues through ComiXology if they're available. As for specific recommendations... From DC, I'd suggest Tiny Titans and Superman Family Adventures, but if she finds those too "baby-ish" then check into the books based on their animated shows: Batman Adventures, Superman Adventures, Justice League Adventures/Unlimited, Teen Titans Go!, Batman: The Brave and the Bold, Young Justice, and Green Lantern: The Animated Series. They're great for all-ages reading, and fun for adults if you're a fan of the cartoons as well. With Marvel, it's a no-brainer -- the whole point of the "Marvel Adventures" line is to create all-ages reading material for the young masses, so pick one and you're set. I'd look into the newer Power Pack books as well; they're well illustrated, and the child protagonists should be easy for her to identify with.
Marvel -
http://marvelkids.marvel.com/comics
DC -
http://dcnationcomics.kidswb.com/
EDIT: Oh! And the Mini Marvels series of comics by Chris Giarrusso. He also has his own kid superhero book called G-Man, that sometimes publishes at Image.