Actually, you can be a sole proprietor with an EIN and a "doing business as" name and still have a Type 1 NPI. I believe the difference is that you are not incorporated (LLC, corporation, partnership, etc) in any way. Even a sole proprietor needs an EIN in order to pay employees and submit payroll taxes for those employees and when you register for that, you can create a "doing business as" name without incorporating. It's just a business, not a corporation. Maybe it depends on what state you're in, we are in NJ and that is how we are set up.
Another question - since I need to apply for both types of NPIs, can I do this online as a single application or will it be 2 separate online applications?