Ubuntu 14.? provides older Qt version than the one you use!
You should either provide Qt libraries which are used by your application or use Ubuntu Qt libraries to build your app if you use same Ubuntu version.
See http://doc.qt.io/qt-5/deployment.html

I finally made it, thanks to your link. I was indeed using the wrong library. I also missed the libxcb plugin but I added it to the project "package" and it now works fine. I was ready to bang my head against the walls.

You have to be sure that static objects are initialized once. If you include into header file they will be initialized every time you include the header file. You can do this using special include guards but IMO is a very bad code style.

I suggest to create a cpp file (or you can do it in main.cpp)