I'm an engineer but worked an IT job as an internship. Did phone calls, customer service, support for engineers, etc... It's not that bad. The greatest obstacle is fear and not enough confidence. Getting my first job was the toughest. I even had recruiters tell me I couldn't get jobs because of my stutter. But I pushed it through it. I been working as an engineer for over 3.5 years now. I sometimes have to communicate via phone but mostly through e-mail (pretty lucky). But I also have to be in a lot of meetings. One thing I noticed is that with my experience I have gained quite a bit of confidence (3.5+ years of experience is not a lot really, I also have almost 2 years internship experience). As you can gain confidence in your workplace you will notice, I think, your stuttering getting much better.