Go for it. My uncle stuttered his whole life but he was a teacher. Students loved him. If you really want to become a professor, don't let your stutter stop you. I know it's scary af, because i stutter too and when i am in front of people it becomes more severe. I stuttered during my class presentations but all the teachers and students were supportive. So although it may sound terrifying at first but it will keep going away steadily. And to be honest I don't think there is any job where you are not supposed to talk, more or less speaking is required. Don't limit your options based on stutter. You can do it.