If you don't want to install Linux, I think the best way is using a Virtual Machine. That's because even if the source code compiles for Linux, how could it be verified to run? You will need a real target environment to finally test your application.
From a complexity point of view, I think setting up a Linux machine (VM or not) and the necessary environment for Qt is a whole lot simpler than cross compiling bug hunting afterwards.
You can install Qt on the installed Linux, copy your project there, compile it and see the results in the real environment. This way you can cope with the minor differences when porting from one OS to another easily.