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: