Ok, just to tell how I solved the problem:

In the file qfiledialog.cpp in functions
void QFileDialogPrivate::_q_navigateForward()
and
void QFileDialogPrivate::_q_navigateBackward()
after
q->setDirectory(nextHistory);
and
q->setDirectory(previousHistory);

I added
emit q->directoryEntered(nextHistory);
and
emit q->directoryEntered(previousHistory);
respectively.

Recompile -> runs

However, I'm not sure, if it's a bug or a feature