For an online business, a detailed and in depth business plan is usually not necessary unless you are trying to combine your online business with a traditional business. For most online business startups, the detail involved with planning a traditional business is not required. However, it would still be beneficial to you if most of the topics were still covered, even if only briefly. Having a written plan in front of you will help you to focus on important aspects of the business.
When writing a business plan you sometimes end up locking yourself away. You might have unique ideas which lead you to seek some isolation and secrecy, or if you are going to be a sole trader you may only have one person to consult namely yourself. But it is fantastic to try and get broader input on your business plan _ whether from a professional, or simply from friends and family whom you trust. I say that because of course you need to be careful with commercially sensitive ideas, as you do not want to pass your plan on to someone in the pub who then starts your idea before you across the road.