I dont really know how to use Inkspace so my method is probably very roundaboutish but the way I used to do it was:

1.- Use gimp to turn the image into solid colours. IIRC the option is called posterize, I would choose 5 coulours for this Image but you have to experiment whats best.
2.-With the colour selection tool, select one colour and make a new png for only that colour shape.
3.- Do the same for the rest of the colours.
4.- Import one of the colour pngs into inkscape and use the vectorize function, I very rarely needed to do adjustments to it unless the shape was complicated.
5.- Remove the imported png and adjust the colour of your new vector object if needed.
6.- Repeat 4 and 5 for the rest of the pngs on the same inkscape document.
7.- Align objects if needed and save to svg.

Hope I explained it in an understandable way, if not, feel free to ask.