You don’t need to leave the job to do an interview. An interview while you have a job is a lot less stressful and I would recommend giving it a go if you don’t like your current job. I dislike them too as I feel I have to doubly prove myself but it is worth persisting with. I stutter frequently where I work. Isn’t a big deal, kinda handy as everyone remembers me. If I have a meeting with a stranger I tell them I have a stutter and they are either supportive or say “ok”.