
versus

As you can probably tell, not a lot of visual difference at first glance, however I reduced a TON of colors on your image -- I took it from 86 colors down to 54, though I'm not sure if the alpha channel was included in that color count or not. Either way, this is a pretty huge difference for not much lost in visibility or appearance.
As you can probably tell, all I did was take some colors with similar value and replace them with other colors of a similar value. I didn't go through the entire sprite because it's getting late here, but I went through most of it. You should look very closely at the differences between yours and mine to see which colors I replaced and which colors I left alone. I did no edits whatsoever to the image or coloring itself outside of color replacement (except for that bottom leg shading, which was bothering my OCD pretty badly).
After messing with this sprite, it must have taken you a significantly longer time creating it than I spent on editing it (which must have been a long time

), but, in reality, a sprite with this style should really not take so long if you simplify the number of colors you use to the bare minimum necessary (i.e. simply avoid having to use dithering by creating a palette with 3-6 shades depending on how much you use a color).
A good rule of thumb is to keep your sprites between 16-20 colors maximum (including transparency) to ensure maximum readability, and blend the colors between one another to ensure maximum unity of the palette. There's nothing inherently wrong with using more colors, it's just that you should keep in mind that the more colors you add, the more difficult it gets when you want to change those colors (especially a shade or value) because you can quickly end up with a huge number of colors just by adding or slightly modifying a shade/hue here and there and forgetting you already have one pretty close to that color/value (thus throwing off the unity of the entire piece). This is what makes the number of colors blow up exponentially, such as what happened in your image.
I admit, my color choice sucks in which colors I kept (i.e. I kept the more grayed-out monotonous/dull colors over the vibrant ones), but I wasn't thinking about that at the time of the edit. Instead, I was simplifying the groups of colors and eliminating banding to show you how to do the same thing with minimal anti-aliasing (AA). I could have simply tweaked the shades I kept to be a halfway blend of the dull color and the most vibrant one (example: the 2 colors that gave the hint of yellow lighting on the grey fur in the original image, for example).
And just fyi, I think your 'flat' color choice for your animation was actually very well made (you obviously have an amazing eye for color) -- it provided much more unity in the colors than r4c7's edit. Once you perfected your motion, THEN give it more form/contrast via lighting/shadow (no need for any contrast, etc. until that time). I'd suggest, as far as the animation itself goes, roll the ball a little more and give it a slight bounce or two to indicate she isn't kicking a beanbag/hackey-sack (unless that's what you were going for, then by all means, you've got it correct).
Hopefully that helps.