I definitely agree that, while helpful, specific domain knowledge is not necessary to begin a Business Analyst career. I would suggest to make sure you master the core competencies needed for Business Analysis: excellent communication skills (verbal & written), meeting/group facilitation skills, analytical & problem solving skills, business process analysis & modeling, requirements elicitation techniques, requirements documentation & management methods, solution modeling techniques (use case models, activity diagrams, sequence diagrams, structured English, decision tables, etc.).
If you are interested in a specific business domain then you can always take courses specific to that business domain - just make sure is something that you have a passion for.
- Adrian