The fact that I've been unable to complete this seemingly trivial task has been annoying me for quite some time now. But this is good news, and I'll try this right away :-)
One more question, though.
The site I've copied was successfully upgraded to 3.3-5 a few weeks ago. Does anyone know if there any known database problems when I install 3.4-0 on top of 3.3-5 and tell the setup wizard to keep the data?