Game development with Qt: where to look first?
I'm currently working on a project providing gaming-specific Qt Quick Components for cross-platform game development, might be of interest: http://v-play.net :)
At the very minimum you will want to look at QGLWidget. You can get an OpenGL program up in a few minutes by deriving from QGLWidget, it will create the window, context, handle mouse and keyboard input, etc. Create a QTimer to trigger updateGL() every 10-15 ms or so and your good to go. I think there is a demo somewhere for setting this up, but it has been awhile since I saw it.
If you want to embed widgets into the window, I would look at QGraphicsView. There is a demo of this called boxes. Just beware the demo is a tad hard to learn from as several classes are thrown into the same file and it might take a few moments of tracing to figure out where the flow is.
Since you are doing a 2d game, you might want to look at using QPainter on top of OpenGL. This allows you to draw primitives easily instead of doing them with OpenGL calls. I never could get this to stop flickering in fullscreen though.
I think that QGraphicsView framework is the best way. Create a QGraphicsScene, some QGraphicsItems for the elements of the game. You have collision detection for free.
Most of KDE games are based on the QGraphicsView framework. It is a good fit for simple game development.