DLL stands for "Dynamic Linked Library" - you can ONLY dynamically link to it. It is not possible to statically link to a DLL. To statically link you need a '.a' file (for GCC) or a .lib file (for MSVC++). This is why you must reconfigure & rebuild Qt if you want to statically link, as those '.a' files do not exist (or exist, but are only stubs).

Last time I looked, there was only DLL file for MinGW.