You'd need a PhD in astronomy to get a job as an astronomer, and if you wanted to go to grad school in astronomy, you should be majoring in physics. With a bachelors in astronomy, you could teach high school, maybe get a job at a museum, or maybe get a job as a research assistant. I know a few people who have jobs as research assistants, but they're hard to find because it's cheaper to hire a grad student to do the same work. Your best bet would be to get a job with NASA, a large lab, or an observatory. These jobs are few and far between, so you'd have to be wiling to move.
Astronomy is a subfield of physics, so yes, it's going to require a lot of math - at least calculus I and II, probably linear algebra and differential equations.
