In order to do what you want, you need to call Java code from your C++ code, through JNI. I don't know any C++ wrapper libraries for this. You will need to get the Java VM from JNI_OnLoad, and when you want to call a Java method you will need to attach the VM to your thread, with gives you a JNIEnv, which you can use to find the class you want and call methods on it. This link should help with the details.
As to whether it is worth it to use QT to develop Android applications, yes, if you need cross-platform support and want to deploy the same application to Android, Linux, Windows, etc. If you are only developing Android apps, then in my experience it is easier and faster to use Android directly.
