What is the advantage of a LLC over a DBA in Louisiana?
First of all, its important to understand that LLC is a legal entity, separate from its owners, while a DBA is just an alias of an existing company (or sole proprietorship).
When properly managed, LLC (stands for "limited liability company"), allows you as its owner to protect your personal assets from any legal action against the company, while DBA would give you no such protection. Since you are in Louisiana I would recommend you to consult an attorney who specializes in Louisiana corporate law to give you more details on the extent of limited liability protection in your state.
Another advantage of doing business with LLC over just doing business as a sole proprietor with a DBA stems from the flexibility of LLC to be taxed as either disregarded entity (or partnership if there is more than 1 owner), S-Corporation or C-Corporation. Since each form of taxation has its own merits doing business under an LLC would give you some strategic advantage tax-wise (however for a more specific tax advise I would recommend consulting an accountant).