First, there is no such thing as getting a degree in herpetology and the day of being a herpetologist is gone. In the past, biology was very focused on organismal level study (mammalogy, herpetology, ornithology, etc.). Now-a-days, you will never see a job listing for a herpetologist as the focus has shifted toward system level study (systematics, conservation, morphology, physiology, etc.). Now-a-days a herpetologist is simply a biologist of some type (a conservation biologist, systemetist, ecologist, morphologist, immunologist, etc.) that uses reptiles as his study organism to answer particular questions in biology. Herpetologists do what they do because they understand the value of answering the questions they examine and love working toward answering those questions and understanding. It does not pay great, requires an incredible amount of school, is extremely competitive, requires constant focus on obtaining funding, conducting research and writing papers throughout your entire carrier, and is definitely not for everyone.
A zoo keeper is what many herpetoculturists (reptile keepers/hobbyists) envision as being a herpetologist. It involves husbandry and propagation of reptiles and amphibians in a captive environment and occasionally in very limited instances involves conservation efforts. Zoo keeping typically pays even worse than true herpetology, with few, if any benefits, but requires considerably less education, although still very competitive.
An exotic vet is a veterinarian that focuses their practice on treating exotic animals, whether as a private practice or as an institutional practice at a zoo, university, or otherwise. It is extremely difficult to get into vet school but once you do, tends to require less schooling than true herpetology. That said, very few vets actually become exotic specialists so the competition at the level of getting into vet school and then becoming a true exotic specialist is very high.
A professional reptile/amphibian breeder requires no education and is simply dependent on your own ability to keep and breed different species, as well as choosing good breeding projects. Professional breeders can sink or swim, but usually sink. There are many factors that go into being successful and things can change in a second and jeopardize your entire collection. Relying on breeding for a living is very risky if you are not very good at it.
As a hobbyist, on the other hand, typically you have a day job and keep/breed as a hobby that you don't depend on. This is honestly the most appropriate choice for most individuals.
What do you really want to be?
Hope that helps.
Chris