I moved a little off from the initial point. I was able to put a breakpoint, at which the program really stopped, and even could be stepped through.
The central idea here is to set the qmake project to the debug mode. In KDevelop, find the QMake Manager popup pane at the right side of the editor. Right click the current subproject and choose Subproject settings -> Configuration ->Build Mode. Change it to "debug". Rebuild the project.
Also, if you compile KDevelop from source, the configure option --with-debug must be enabled.
However, the debug stepping refuses to move on once the end of the current function is reached.