Dear Kavin,
You can directly become a stock broker either by purchasing your own trading rights (which requires an investment of i guess a crore), or through a franchisee of any brokerage house (which doesn't require a huge investment). Anyone right from a dropout to the most qualified person can do this and become a stock broker. The success achieved after being a stock broker is purely a matter of your own efforts than degree. It will depend upon your understanding of markets (when to buy and when to sell is not tauth in any course or book so its not like anyone has an edge over others), you ability to network with people, luck etc.
If you want to work with a stock broking firm, there are many profiles and you may clarify what you want to do. In a brokers office, you will find some people sitting on the system, executing orders on behlaf of clients, some will be ensuring risk management - monitor client limits and compliance etc, some would be sitting and interacting with new people who wish to open accounts, some will be doing book-keeping work, some will be doing research about companies and their managements and figuring out investment opportunities, some will be looking at past trends of prices and try to prediuct future prices and there are many other things which are done in a brokers office which people from different backgrounds do.
Like in CAs, the doamin area is accounting, auditing, taxation, it is surely difficult for CAs to find jobs outside these three areas (PS - I said only "difficult" and not impossible). Its always difficult to get a change. See even in case of engineers, they get into finance mostly after doing an MBA only.
Knowing what to do early in life is surely quite difficult thats what even Mr. Buffet says.
You may refer to my blog and read articles on personal branding, "the buffet style of success" etc. I have shared my insights on what it takes to achieve what you want.