You use 27 colors which are pretty close to each other.
Recycling colors is key to keeping your palette small which makes recoloring easier and is generally less of a pain to work with.
I knocked it down to 9 colors and also considerably lowered the saturation.
Laser green isn't a nice color to look at so try to keep the saturation low and also vary the hue a bit between shades.
Shadows generally become colder while highlights become warmer.
As for the thing itself, deers are way bulkier than that, even female ones and they also have noses and mouths so try to look up some references there.