Is it possible to separate an image into layers?

Someone designed pixel art for me but didn’t save the files into layers. The background is a set colour, as well as the drawing. Is there anyway to easily select the outline of the sprite and make that its own layer?

Select the background color using the Magic Wand with “Contiguous” turned off (so it also gets any isolated background pixels) and delete it (or cut it out into its own layer if you want).