That depends on how you decide to distribute it. If you distribute as closed source (binary only), then you must comply with LGPL license and so your application must be dynamically linked.
Else you distribute under GPL license and release the source code, which allows static linking.

Either way, any modifications you make to Qt must be made open-source - anyone who wishes to do so must be able to build the exact same DLLs (or static libraries if you use them) as your program requires.