Legal Question in Business Law in Georgia

So long as you only ship to another state in response to orders placed via your website, then generally-speaking, no, you do not need to register your business in another state or get a business license for another state.

However, what you need to be most aware of are what are the state-level tax implications of your shipping to these states. Multiple-state taxation can be a very complex subject so I urge you to contact an attorney to discuss your specicific circumstances.