I'm going to rat out my group to the professor that they haven't done any work
What are you going to tell the professor?
They've been sitting around and having fun since the beginning of the semester.
You are right to let the professor know what's going on. It's not fair to be the only one contributing as the rest of the group mess around.
I don't want you to fuck over my business so back the fuck off.
It's always great to be assertive and talk to the group first by pointing out there lack of contribution. However, if they are not  positively responsive to your feedback, you should let the professor know so that he can change your group or create new rules.