How to write a webkit application where a javascript will invoke a QT C++ methods?

[ChrisW67]

You appear to be building using Qt5. The error is repaired with:

QT += webkit webkitwidgets

QT += webkit webkitwidgets

To copy to clipboard, switch view to plain text mode 

Webkit requires Gui.

Since you are using Qt 5, you should be reading the correct version of the docs:
http://qt-project.org/doc/qt-5/qtwebkit-bridge.html

The next upcoming challenge I thinks is how to relate a java script present in any folder of my FC19 to invoke a QT function defined in the above program. How my javascript will know the path to pick the application. How it can be done?

You can only use the QtWebkit bridge when the HTML/Javascript is loaded into a QWebFrame in a Qt application (i.e. using QtWebkit). The HTML loaded into an arbitrary browser is not magically going to launch a separate Qt program and connect itself somehow.