Sure. 'The Tale of Despereaux' is a great 4th grade quest short story. It's about a small mouse named Despereaux who goes on a quest filled with adventure and danger. He has to overcome his small size and the many obstacles in a castle to save the princess. Then there's 'Stuart Little'. Stuart is a mouse - like boy who has many little quests in his life, like trying to find his lost friend and having various adventures in a big world made for humans.
One popular 4th grade quest short story is 'The Magic Tree House' series. These stories often take the main characters, Jack and Annie, on various quests through time and different places. Another could be 'Charlotte's Web', which is about a pig named Wilbur and his friendship with a spider, Charlotte, and the quest to save Wilbur from being slaughtered. There's also 'The Fantastic Mr. Fox' where Mr. Fox has a quest to outwit the mean farmers.
Well, 'James and the Giant Peach' is a wonderful 4th grade quest short story. James embarks on a quest when he enters the giant peach. He meets all sorts of strange and wonderful creatures inside the peach and they have to journey across the ocean together. Also, 'Because of Winn - Dixie' has elements of a quest. Opal's quest to find out more about her mother while befriending a dog named Winn - Dixie is really engaging for 4th graders.