Build for Linux & Apple
Is it possible to build a Qt GUI application under Windows, but the target platform is Linux or Apple? If that is the case, which compiler should I use?
I don't think this is possible exactly the way you want it. You can build your app on "one Mac OS X version and deploying on all others versions of Mac OS":http://qt-project.org/doc/qt-5.0/developing-on-mac.html#deployment-compile-once-deploy-everywhere.
Check "this article to learn how to build Qt apps for Linux/Unix":http://qt-project.org/doc/qt-5.0/deployment-x11.html
The presentation "Application Development on Linux for Windows Developers":http://qt-project.org/videos/watch/application_development_on_linux_for_windows_developers might also be useful for you.
I am not aware of anyone providing a cross-compiler that enables building on windows for Linux. Since "Linux" differs a lot from one distribution to the next that is most likely too hard to do in a generic way...
Many Linux distributions ship with a mingw which can be used to cross compile from Linux to windows though.