In my opinion, a business plan or some kind of plan should be made for EVERY project. Without a plan, you don't have direction. Without direction, you can easily get caught up doing things without experiencing real results. A business plan will tell you what resources you need, where to get those resources, a steady timeline, budget, and so much more. So, yes a business plan is essential for any project.
You should make a business plan because then you will have all yours goals placed on paper. You will have all written and going with that plan. It is better to have all planed before you start your own business than to think about the next steps after you finish some part of the work without plan.
Is this project some kind of business venture for which you'll be seeking financing from a bank or investors? If so, then yes, you need a business plan. If this is a one-time project that has a start and a finish, then you need a project plan that includes: - the project's goals and objectives - scope - tasks that need to be accomplished - timeline - resources needed - budget - risk assessment - communication plan