Install qt. If you've actually written something with the library, how on earth do you believe it could run without that?
Clues to this mystery are highlighted red.
int main( int argc, char **argv )
QApplication a( argc, argv );
You might be able to make some kind of static executable that includes the Qt libraries, but you will now have like a 50-100mb exe for "hello world" (if this is even feasible, which I am not sure). Very bad idea. You could include the Qt libs yourself, altho there may be licensing issues there, and it is also pretty silly.
Qt is easily available for all linux systems, you click your mouse in synaptic or whatever and it's done. Don't get paranoid about it. Your app "requires Qt 3+".