Your image is an Indexed png and the colormap shows 255 black entries and 1 white entry. You do not get semi-transparency with indexed images, it is either all or nothing, the equivalent is dithering.
For the antialiasing filter to work, change to RGB colorspace Image -> Mode -> RGB
If you desperately need the image in indexed mode, change back to Indexed Image -> Mode -> Indexed and in the export dialogue enable dithering and maybe 12 colours gets something like this:
edit I should add, If you have your original in RGB mode and a transparent background, the easiest way to apply a blur as Blighty's post is use the tileable blur with a value of 2.
For the antialiasing filter to work, change to RGB colorspace Image -> Mode -> RGB
If you desperately need the image in indexed mode, change back to Indexed Image -> Mode -> Indexed and in the export dialogue enable dithering and maybe 12 colours gets something like this:
edit I should add, If you have your original in RGB mode and a transparent background, the easiest way to apply a blur as Blighty's post is use the tileable blur with a value of 2.