This is pretty much correct, but you have to change a few settings to delete only the white background:
Select "background eraser"
At the top set "limits" to Contiquous, "Tolerance" to 50%, Tick "Protect Foreground Color" and set "Sampling" to Once
Set Color of foreground to Red and background to White and that should erase the background with deleting the image itself
Save as Png or Gif