I'm also learning Qt and tried to find a way to use Unity API in Qt , I could only use Dbus API , but no luck with Quicklist since it needs a DbusMenu and I do not know how to implement that (still learning :) ).

This is the example I created for my self and I hope it's useful for others .
Maybe Unity devs can help to correct / fix / add new code (quicklist) to it :)

/*

    Unity Launcher Dbus API exmable for Qt

    foxoman [gplus.to/foxoman][[email protected]]



    https://wiki.ubuntu.com/Unity/LauncherAPI#Low_level_DBus_API:_com.canonical.Unity.LauncherEntry



    First step : add this line to your Qt project file .pro

     QT       += dbus

*/



/* I will run this example as Qt console apps */

#include <QtCore/QCoreApplication>



/* Include Qt Dbus required */

#include <QtDBus>



// Qt Main Method

int main(int argc, char *argv[])

{





    /* Qt console Main Loop [ in GUI application the Main loop is QApplication ]

        Unity API need Main Loop to run */

    QCoreApplication a(argc, argv);





    /* Create Qt Dbus Signal to send Dbus Message to unity Dbus API

        signal com.canonical.Unity.LauncherEntry.Update (in s app_uri, in a{sv} properties)

    */

    QDBusMessage signal = QDBusMessage::createSignal(

     "/", /* Path */

     "com.canonical.Unity.LauncherEntry", /* Unity DBus Interface */

     "Update"); /* Update Signal */





    /* app_uri

       Desktop ID ex: firefox -> need to be pined in the launcher to see the effect

    */

    signal << "application://firefox.desktop";





    /* properties : A map of strings to variants with the properties to set on the launcher icon */

    QVariantMap setProperty;



    /* A number to display on the launcher icon */

    setProperty.insert("count", qint64(80));



    /* show count */

    setProperty.insert("count-visible", true);



    /* progress bar count must be float between 0 and 1 (mean from 0.00 to 0.100)*/

    setProperty.insert("progress", double(0.80));



    /* show progress bar */

    setProperty.insert("progress-visible", true);



    /* Tells the launcher to get the users attention  */

    setProperty.insert("urgent",true);



    /* Pack the properties Map to the signal */

    signal << setProperty;



    /* Send the signal */

    QDBusConnection::sessionBus().send(signal);





    return a.exec();

}

download the example here
http://ubuntuone.com/1SLDPcN9OhrU6LD1wgDs3r