I do not have a stutter but my fiance does. She probably stutters almost every sentence. She completed her bachelors degree in biology and found a job working as a lab tech. It's so doable and you'll meet some of the most understanding people in universities. Working in the field of medicine and science you'll meet many intelligent individuals who will see past your stutter. You'll meet some bad apples along the way but that's life, and your entitled to live yours the way you see fit.