Something really fishy was going on when dragging the 'Drag me' folder in the X11 test area onto itself.
Instead of using a custom QStandardItemModel with a QListView, use a QListWidget, which comes with its own model that does not allow dropping items onto other items, but It is still possible to move the icon.
Fixes https://bugs.kde.org/show_bug.cgi?id=346900 and https://bugs.kde.org/show_bug.cgi?id=366113