First off I am no attorney, so dont take me word for word. If you are claiming to have a business, IE a business name, you need to register it. Why? Just one example, what if that business already exsists... you call your self that name, you have commited a serious crime. Different states have different rules. Some states are fine with you selling under a perticular dollar amount with out a business liscense and paying sales tax... some are not. But you still cant call your self something you are not (A business name). Liability wise, you are a fool to not contact an attorney and have them draw up (and talk to you about) limited liability papers for your business. When you deal with genetics and thousands of dollars in snakes, you need to protect your personal self against law suites.
Put simply, yes you need to register it. Take a class on small business so you know how to file taxes. I will give you some advise, if you are not planning on pumping some money and time tword this, dont get into it. Its so easy to just say they are bred by you and not by a business.