Your manager knows you stutter but trusted you to occupy the new role because she knows you can do the job. I also stutter and have learned to improve by doing things I ordinarily would not do out of fear of my stuttering getting in the way. I presented a case study for a spot on the case study team for my Uni. It could have gone better, I stuttered, but I did it. I did not get in, but I conquered that fear. It would be best if you tried conquering yours as well. You do not want to be a tasker/freight for the rest of your life.