The Dark Hills Divide is the first book of the Land of Elyon series by Patrick Carman. The whole set of Alexa’s adventures qualify as a Girls Underground story, but I will just mention this initial book to begin with.
Alexa, 12 years old, longs to go beyond the walls that enclose the towns she knows. Suddenly she is thrust into a world of mystery and danger, and must journey far from her home in order to save it. She is accompanied by a dwarf and talking animals (two very frequent archetypal companions of the GU). Alexa must uncover who leads the threat against her country, and thwart the rebel forces he commands, before they enter the city and destroy it.