Drawing animals is like experiencing the animal as it was right in front of you. To me painting an animal usually gives me more insight of the details on the animal's proportions that I would otherwise not notice from just looking at a picture.
Is it really so hard to do a nice cat painting or nice dog painting for that matter? That is a question I get a lot. My answer is that only patience can make a great drawing. Because if you are not willing to spend many hours just getting the proportions of the sketch right, shading it right or the lights right the result will be not very impressive.
My best advice on how to improve your animal drawings is simply to spend more time on them. For example if you are not fully satisfied with the eyes, don't just continue with the drawing and hoping that the eyes will get better by themselves! No, look at the eyes and don't give up on them until you are fully satisfied with them, then move on to the next part of the animal drawing.
Another advise is to not have the attitude of completing the painting / sketch tonight, because this will just make you rush the whole animal painting and get you frustrated that it is taking longer than you expected.
Instead work an hour here and an hour there and sooner than you think you will have completed a great painting of that favorite animals of yours!