If it is urgent then you are far better off finding a Windows machine, installing the Qt SDK on Windows, and building from source code there.

The alternative is:
  • Build a MingW cross-compiler tool chain
  • Build any libraries, including Qt, your application needs using the cross compiler
  • Configure Qt, your IDE, and your project to use the cross compiler
  • Build your application using the cross compiler

MXE (M cross environment) may help you do some of this.

Then you still need a Windows machine to run and test it, which brings me back to my opening point.