Should I do a group project on my own? If so, how?
A group project in class isn't the same as an assignment at a job.  The teacher doesn't need this project done and isn't paying you to do it.  The project is assigned for your benefit and it was assigned as a group project because not only is course material to be learned but also teamwork skills are to be honed.  Use this opportunity to practice working with a group.  Hone your interpersonal skills and see how good you can make the result in spite of having less skilled teammates.  That's really the point of group projects.