Thinking of becoming a speech therapist to help people like me. Is this possible since I stutter?

Thinking of becoming a speech therapist to help people like me. Is this possible since I stutter? I’m going to be a senior in high school and my girlfriend has hooked me on the idea of becoming a speech therapist because she said that I’d be able to relate to people with speech impediments and they wouldn’t feel out of place. I just want to help people like me because I know what it’s like.