Qualifications
The most common way to become a literary agent is to work your way up the literary agency ladder (source). But here's the catch. This doesn't always work.
Most agents start out with a college degree and either take an entry level job in an agency's mailroom or, if they're lucky, covering a junior agent's desk. Sound fun? Well, it's notoriously not. With your bachelor's degree, or even your business or law degree, can find yourself answering phones, ordering lunches, and delivering mail for years before you actually find yourself managing your own clients and desk.
Your law or business degree will help you down the road, but until you've learned the ins and outs, who's and what's, and how's and where's of every single angle of the deal-making machine, you should expect to be treated like a know-nothing who can't be trusted to tie his own shoes.