Where can I see the demo of Quick Index?

I am not familiar with that wordpress plugin.
So in order for me to answer your question I would need to figure out how that plugin works by reading the documentation and trying it out.

But wait, I am not the one that wants to know how that wordpress plugin works. You are the one that wants to know how Quick Index works.

So: read the documentation and try it out.
docs4.regularlabs.com/quickindex

There re multiple examples of it throughout the documentation.
Also the 'On this page' thing on the right side of many of the documentation pages are created with Quick Index.

Just download the free version and try it out.
Want to know how it works: read the documentation.