It isn't true to say that Carley does nothing special with her gun. She is seen killing more zombies than any other member of the group, and she saves Lee and Clem more than any other member of the group.
People also like her because for the most part, she is also a moral character.
When you first meet her, along with Glenn she rescues Lee, Clem and Kenny's family when they get surrounded by zombies outside the Pharmacy, even though Lilly and Larry were against it. She shows concern for Clementine and will refuse food when supplies are low, telling Lee to either feed Clem first or hold onto it in case Lee or Clem gets hungry later. And she is the first to give Lee a second chance on his past as a convicted felon, and keeps to her word not to tell the rest of the group. Later she sticks up for Ben, who was just a kid, when Lilly starts throwing around accusations without proof.
Her one moral failing was perhaps in not wanting to rescue the trapped girl at the motor inn. But considering the circumstances, it was at least understable. And everyone is allowed a mistake or two during the Zombie Apocalypse.