There are undergraduate journals that are available for ug publishing.
Here is a call for one.
The Valley Humanities Review is currently seeking essays in the humanities for publication in its Spring 2010 issue. We seek essays of high quality, intellectual rigor and originality that challenge or contribute substantially to ongoing conversations in the humanities. Topics may include but are not limited to: literature, history, religion, philosophy, art, art history and foreign languages. VHR is committed to undergraduate research and scholarship in the field; therefore we only accept submissions by current or recently graduated undergraduate students. Our reading period runs from September 1 to December 1 of each year. All submissions received outside of those will be returned unread. Essays should be between 3,000 and 6,000 words in length, be free of errors, and have an original title. Submissions may be emailed to firstname.lastname@example.org. Please visit our website.
It would be interesting in a literature course to make this the final paper that the entire class moves toward. If I were teaching a lit class in the fall, I would do this.