You're using the word "incorporate" incorrectly, which was my original point. To incorporate means to start a corporation. Therefore, registering a sole-proprietorship is, by definition, not incorporation.

The more general term is "register", which applies to the three forms of business: sole-proprietorships, partnerships, and corporations.

What you're thinking of is a business name registration. If you do business as your exact name, you don't need to register a name. If you make more than, $30k (I think), then you do need to register for a GST number.