How do I give these images a white background? Making product shots for wooly items

I've made some plush toys out of a wool fabric that I am making product shots for. They need a fully white background, but the fine details of the wool keep getting lost when I use the magic wand tool.

I'm intending to make the final image a banner for my website advertising my services (freelance toy designer so these need to look really good!). It's the first thing that the customer will see on my website, so I'm trying to make as good a first impression as possible. How do I give these a transparent / white background that picks up the fine details of the edges and doesn't look too "toothy"? Is my photography suited to doing this? The background is quite grey as opposed to white, so I'm wondering if that's going to pose a problem.