Why study Developmental Psychology?
1) Excluding obviously applied degrees like education, engineering, etc. all bachelor's degrees are equally useful/useless. That is, they qualify you to do any job that requires a bachelor's degree. Just as 40 years ago, you had to get a high school diploma because most jobs said "must have high school diploma", now they all say "must have college degree". The expectation is that you will arrive at your job with a core set of college level abilities (reading, writing, analysis, self-discipline, attention to detail, etc.), and the company will give you whatever specialized training you need. In that sense, a degree in psychology is as useful as a degree in philosophy, history, or biology. Hence, you may study developmental psychology simply because it interests you, and with no intention to take it further.
2) That said, there are many things that a degree in developmental psychology should make you well suited for. It is an excellent degree from which to go into teaching, counseling (especially with children and adolescents), school psychology (i.e. administering intelligence tests, designing customized programs, etc.), day care, social work, public policy analyst or lawyer (specialized in child law), etc. There are also quite a few businesses that specialize in programs designed to enhance the lives of gifted or disabled children, not to mention the host of normal medical things geared towards kids (i.e., child surgery wards, dentists, etc.) all of which employ someone whose job it is to do the stuff for the kids that you don’t normally have to do for adults. Also, let’s not forget all the marketing and advertising geared towards kids, as well as children oriented educational TV, games, museums, etc.
Honestly, one can get a developmental psychology degree and know almost nothing, but if you are motivated, and push yourself (and your professors), you can come out knowing quite a bit towards some specialty. If this is the route you want to go, then you should also try to do summer internships or part-time jobs that interface with your hypothesized career path. This will both enhance your resume and give you a real view of what the job is like.
3) Oh yeah, and then there is always the career in research. Of course, for that you need to be psychotically grabbed by the research bug. I recommend you avoid it in all earnest. If you find that no such efforts are successful, and you keep coming back to it anyway, then that is the best sign that it is the life for you. My work currently specializes in infant perceptual development. You can imagine that there are few direct commercial applications, and hence no big bucks in my future. There are some long term medical implications with regards to autism, etc., that keeps the National Institute of Health interested, and some cool theoretical implications that keep other scientists interested, but it is often a bit awkward to explain what I do at family reunions.