Actually it's not so big problem. You need to check you include directories and add (path_to_qt_headers)/QtCore, (path_to_qt_headers)/QtGui and directories for other modules you are using. According to your problem description you have added only (path_to_qt_headers) itself.
If Qt set up correctly both #include <QObject>
and #include <QtCore/QObject>
should work but second one works in more cases. I remember I saw some notice somewhere in the Qt documentation that it might be better to using second include style. At the same time this long include version is recommended in the KDE coding guidelines.
For myself I preffere to follow #include <QtModule/QClass>
include convention