Copying baseGNU to the virtual disk works. Even booting got through but when I try to run native-install it never gets to the very end. First time it froze on sed package, the other time on sysv-rc.

How much memory did you configure for the QEMU system? It may simply be -- I've seen this myself -- that the system runs out of memory, as at the native-install stage (I think at least) swap is not yet configured and enabled. What I've been doing is: boot (with -s), MAKEDEV hdWHATEVER in /dev/ for the swap device, run /hurd/mach-defpager, followed by swapon /dev/hdWHATEVER. Does this help?

Thank You very much, more memory solved the freezing.