My boyfriend has a stutter and isn’t a teacher however is a mental health nurse, being able to communicate effectively is absolutely crucial in this job (I’m a mental health nurse it too)! He has to talk all day long every day to people who’s poor mental health makes it harder for them to be able to understand and retain information. I think having a stutter has given him a lot of skills and insight which possibly he wouldn’t have if he didn’t have a stutter. This sounds like something you are passionate about therefore you should absolutely go for it! Having a stutter does not have to hold you back or prevent you from doing something you love. I hope you don’t mind me commenting as someone who doesn’t stutter I know I will never fully understand.