Nimm anstelle eines Labels ein TStaticText und mach's so:
(ungetestet)
Delphi-Quellcode:
procedure TForm1.Image1MouseDown(Sender: TObject; Button: TMouseButton;
Shift: TShiftState; X, Y: Integer);
const sc_dragmove = $f012;
begin
ReleaseCapture;
TWinControl(Image1).perform(wm_syscommand,sc_dragmove, 0);
TWinControl(StaticText1).perform(wm_syscommand,sc_dragmove, 0);
end;