The model looks nice! I ran into the same material problem for my dog model (see this post). In the renders I posted, I did end up using a hair particle system, but while I tried to make the model game-ready, I ended up giving the model a furry texture by creating my own bump map and painting it with special stencils I rendered from a flat sheet of fur. If you can do that, it should be easy to make a normal map with simple, open source tools like AwesomeBump.
Here’s what I ended up getting in the EEVEE viewport.
In renders especially with Cycles it looks a lot better IMO. I hope this helps!