Read: Deploying Qt Applications and the numerous time this exact question has been asked here.

My recommendation is that you use dynamic libraries unless you <i>must</i> have a static executable. The level of effort involved in producing a static executable, including all your dependencies, is comparable to writing an installer script for NSIS or another similar tool. A wholly static executable is complicated greatly if you use QTHelp, QtWebkit or Phonon which impose LGPL requirements for end-user relinking (even on commercial licence holders).