@Toony-Days This is my process.
Think of what the character is going to be personality wise, then find a movie with a character that is similar to that personality and screen shot poses/expressions that represent the personality you want. Then do gestures drawings of the screenshots, then put the reference away, and use my gesture drawing as reference to do another gesture of, trying to capture the essence of the character. Each time you do a gesture, try to exaggerate the poses or expressions. Once you've got something you like you can apply it to whatever animal character you've got. I would read up on anthropomorphism and maybe Cartoon Animation (really good book). At the end stage, when you have a sketch that captures the essence of the character, pose and expression wise, you should start refining it and start thinking about how you can make it more appealing by adding different design principles like colour theory, big medium small, 70/30, guiding lines, silhouette to name a few. Silhouette is probably the most important one for a clear character design I think. You shouldn't change your design too much just to get all these principles in but if you see an opportunity for one I would go for it. I would also gather a range of other artists' work to see how they solved the same problem, even renaissance painters looked at masters to study from. I would only do this at the end stages though so that you're not too influenced by them.
I could say so much more but there are so many great sources out there for this. The number one thing I would focus on while you're doing this is drawing as much as you can. The more you do it the better you'll get. Kim Jung Gi fills 5 sketchbooks a week. This seems impossible for most people but I think it's something everyone should aspire to achieve.