Well.. I dont use fedora, so dont know which version of qt comes with it. Anywayz, when you download kde, get all the files in the respective directory. Things like qt, kdelibs, kdecore, kdebase, etc. are absolutely necessary.
After downloading all that, do an rpm -Uv *.rpm instead of rpm -iv. That "U" is to upgrade packages. "rpm --help" for details.