It takes restraint not to re-post everything Jillian writes on her blog over here. But take a moment to check out her advice on drawing animals in this post – “There is no formula to trick to drawing animals, or anything else for that matter. Only observation (ideally from life) and practice will give you a fundamental understanding of structure and form.”
Check Jillian’s illustration gallery here to see how uses animals in her illustrations regularly to evoke motion and emotion to great effect.