Install Qt 4.7, download Qt Creator 2.1 (http://qt.nokia.com/developer/qt-qtcreator-prerelease/) and follow the tutorial (http://doc.qt.nokia.com/qtcreator-2.1-snapshot/creator-qml-a...), it's really a great tool.

As a QT programmer already, I'm excited by this approach to creating 'hybrid' applications.

Not immediately clear:

Where and how could I deploy an app like this? What are its dependencies? Does it run in the browser or an OS? How do I set up the environment to compile it?

You need the QML runtime (http://doc.qt.nokia.com/4.7/qmlruntime.html) which you can embed in any Qt C++ app or deploy on mobile devices. The idea is that you code the app in C++ and code the user experience with this language, writing bindings to your models on the way.

Another interesting connection between Qt and JavaScript is QWebKit which allows you to run web applications (HTML/CSS/JavaScript) within a GUI widget.

QWebKit also allows you to add custom GUI handlers to events like clicks to certain links, or to prefix each loaded page with a certain piece of JavaScript.