Conducting research as an undergraduate
To answer your questions directly, yes, you can submit for publication as an undergraduate or as a completely uneducated person for that matter. Science and other scholarship is about the work, not the author's credentials. It will be credible if it is credible, independent of who you are. But it needs to say something new and interesting to have credibility. It is more, much more, than going through the motions of carrying out a study. 

The only real reason for having a professor involved is that you can take advantage of his or her experience in doing research, writing it up, and getting it published. The name and credential is, as mentioned above, not the important thing. Likewise, a joint effort with peers is valuable since it is more likely that a few minds working on a problem will notice issues that need to be addressed and come to a better result. Other than that - little or no effect. 

However, if you don't have any experience in doing this, it is pretty unlikely that you will be successful in your first attempt given the time constraints. Learning to do research and get it published, like any other learning task requires both practice and feedback. Many people, even with more educational background than yourself will struggle to reach the point at which it can be done with any facility. Most of them (a few exceptions) have the advantage of being able to bounce ideas off of much more experienced people - feedback. 

Of course, if you do write something up and submit it to a journal or conference, it will be reviewed. If it has any validity at all you will get feedback from the reviewers. Hopefully it will be constructive, but sometimes it is disheartening. But it is better to get some local feedback before attempting publication, just so you get the practice and wind up submitting things that need less "polishing" to actually be published. 

Like anything, though, you get experience through practice. Early attempts may be successful, but for most it takes a few tries. But the practice needs to be tempered by feedback. 

If any of your professors have published material, you might want to approach one of them with some idea for a study. Ask if they can guide you and give you feedback. Even if you don't reach the publishing stage, that feedback will be valuable in figuring out how to approach research and how to make it presentable. Someone with more experience is also more likely than yourself to have an idea about what sorts of things are ripe for research. It does you little good to work on questions already answered and it normally takes a lot of study to understand where the research "edge" is any given field. A more experienced person can help with that, showing you what is the most important thing to look at.