Binary with no dependencies
How would I go about doing this? I see the .lib files that would replace the dynamic libraries in my Qt folder so I believe I can do static linking.
The pre-compiled Qt binaries you can download have been built as dynamic (shared) libraries. The .lib files you see in the "lib" folders are import libraries - not static libraries! Those are linked into your program file in order to use the Qt DLL files. If you want to link Qt as static libraries, you'll have to compile Qt from the sources yourself. Just be sure you call "configure.exe" with the "-static" option. You probably want to add "-release" too.
For what it's worth, this is what I do:
Keep in mind there are license limitations to using static Qt builds. Commercial application would either require to be open sourced or a commercial Qt license.