I work with a genetic counselor and it seems you can do much with that particular degree. Right now the counselor is helping us to find and interview families for a study we're doing on cancer disposition. So, she works at a desk in a lab, and talks to different family members, makes family trees, determines who has cancer and what kind... It's more of a research job.
Before this, she did pre-amnio counseling. She talked to older women about some of the risks they face (showing them karotypes, explaining trisomy 21, etc)
Some genetic counselors advice Jewish women on what diseases they are susceptible to, and suggest proper testing.
PM me if you want more specifics... it's a varied career and lots of people involved arehappy