There is no such thing as just blanket employment authorization unless you are a green card holder.  Until then, your employment authorization is tied to an employer.  IF you are qualified for a different type of work visa, such as H-1B (requiring at least a bachelor's degree ), and you find an employer who offers you a position and successfully petitions for your H-1B visa, then you will be able to change status from J-1 to H-1B.