you can do this with a white background too i just used this one
first you hit the shrink (also make sure you have the whole thing selected)

then set it to like 15 (you can experiment with it)

you will get something like this

then click grow

set it to like 10 (don't go over the shrink or it will cancel)

you will get something like this

then click invert

will get something like this

then add alpha channel by right clicking the layer

then press delete and your done :p
Ending result: