New layers from line sections?

Question

If I have an outline on a transparent background, perhaps like a bunny, with the outer line and internal lines defining sections. I want to make new layers out of those sections filled in, different layers for each section. The way I've been doing it so far is to create a new layer, then either fill over the area and erase what isn't in the section I want, or else draw over the outline of the section and flood fill it in. Either way this takes a long time. I tried filling in the section with flood fill, using magic selection, and make new layer from copy, but the problem becomes that the edges of the inner section aren't right to the edge of the line and this is visible with what I'm filling with (often solid colors), which is why I drew over the edges on another layer because I can place the outline on top and the underside isn't seen.
Is there a faster way to do this?

Answer 1

Outline starts like this:
Goes to this, with each color on a separate layer:
The yellow layer looks like this:
The whole thing looks like this when finished, colors still on separate layers: