No, you dont need to be a graduate student to be able to teach. You only have to graduate with your bachelors degree in teaching, then apply for your state's teaching certificate once you have proved that you finished the bachelors program for teachers.
Make sure that you want to be a teacher before declaring and finishing the major. I know a few people who went through 4 years, and hated student teaching..so they changed their major. My suggestion is to go to a classroom a few times to make sure that you like the thought of being a teacher. If you do, great...if you think it would get annoying...change your major!
Best of luck!