I think my main suggestion would be to start by trying to draw a more familiar shape. You know, something more recognizable. With this particular image, especially with so few colors, it is hard to tell what is happening. Even simple objects can be tricky when it comes to pixel art. Take this barrel as an example:
Depending on who you are you might choose to stop on the bottom left one and say "That wood there is obviously wood, I don't think i could possibly add more detail with so little pixels so I'll stop here". Which is a perfectly reasonable point of course, but the bottom right barrel shows you that there was so much more you could have done with the wood on that barrel and even a single pixel here and there can make all the difference.
To be honest, I've never even attempted dithering and still shy away from it. I think that it may be due to the fact that most of my work is at a lower resolution and that it is generally a technique used on higher resolution art to give it more of a retro look.
But anyway, I would definitely suggest starting out with something more familiar that you will be able to recognize when it is finished. You will much more easily be able to tell when something is wrong with it because of how you are imagining it to look.