I think your project file is wrong.
So you want a GUI application, but you remove the GUI module by
QT -= gui
Have you tried creating this application with the project start wizard? I think you may have selected the wrong type of application.
EDIT
If you want to build a project without the gui module, you need to exclude it with the "-=" operator. By default, QT contains both core and gui, so the following line will result in a minimal Qt project being built:
QT -= gui # Only the core module is used.
So, you only have the core module. Source: http://qt-project.org/doc/qt-4.8/qmake-project-files.html
Try deleting the
QT -= gui
line, since "Note that QT includes the core and gui modules by default". See source.