Take a look at the file Properties->Details of "QtCore4.dll" it uses to see what Qt version it is.
Go to Qt website download page and get the matching version.
There are both full source and compiled distributions there.
You will probably have to rebuild it to match your application's compile settings.
For instance if you see the application is using "msvcr100.dll" then you know it's using "Visual Studio 2010".
This way you might be able to build compatible import libs to use from an injected DLL, and the example/samples should be close to your target for examination.
You should read up on at least the basics of Qt.
You say it's using a QList then take a look here: http://qt-project.org/doc/qt-4.8/qlist.html
Although that is not a widget, it must be some sort of list or list view type based on your description.
Look at the Qt imports in the application. Like at instances of the "QWidget" ctor for example to find out where various widgets are being created.
If you can inject a DLL you can probe by setting a hotkey to call static methods "QApplication::allWidgets()" or "QApplication::topLevelWidgets()" to get list of all the controls with info facilitated from accessors like "windowTitle()", etc.
The logical/obvious places to look are at the control that is being manipulated, and the mouse click signals/events that it has setup.
You just got to start digging in and break things down.
Don't know your experience level, but in reversing often "the hard way" is the right and, or, the only way..