assuming you took some care to use portable code, i.e. use Qt API everywhere to hide platform specific code or #ifdef, the process is simple.
An example to copy a project from windows to linux:
1) delete debug/release folders
2) delete Makefile, Makefile.Debug, Makefile.Release
3) delete object_script*.*
4) delete <project>.pro.user
5) copy the entire folder
6) open the <project>.pro file with Qt Creator on linux
7) build all

note: if you link any 3rd party libs, then you need to specify the differences in your .pro file like so (example):
unix:LIBS += -l/location/of/lib/linux/libwhatever.a
win32:LIBS += c:/location/of/lib/win/libwhatever.a