The following things are possible:
1) You may not have installed the Qt libs. Try looking for an RPM from www.rpmfind.com
Alternatively u can try using the package manager. (Run system-config-packages from the "run" command or a terminal). Go to the appropriate section (probably KDE or something). Here you can check if the Qt libs are installed. If necessary u can install them.
2) If the Qt libs are already installed, then the kmid installer/compiler is not able to locate it in the default path. Somehow, you may need to change the path, unfortunately I dont know how. But if u know where the "configure" program is searching for the libs, then u can make symbolic links into this folder.
The best solution, according to me, would be to use RPMs instead of installing from source. U can download RPMs from the sites I have mentioned above. Kmid RPM is probably there in the Fedora CDs.
Note: I'm a newbie myself, so dont blame me if your CPU gets fried.