That's not a great image. Like you say, Refine Edge is not going to give you a great result, and the rabbit is out of focus and the lighting flat. It's even particularly big, (unless you downsized it to upload to this forum) Seeing as you found it on the internet, I'd be strongly inclined to go find a better example.
There are several hits with rabbits on white backgrounds, which will make selection so much easier. GOOGLE
But if you really want to use Refine Edge on your example, have a look at this Martin Evening tutorial, which is the best of its kind I know of for that sort of subject matter.