There are two components to the light being reflected off the fur. The predominant one is likely diffuse scattering. A polarizer won't help with that. There may be some more "reflection" looking sheen, especially if the light is coming from somewhat behind the cat. That probably is polarized, so a polarizing filter should be able to accentuate or attenuate it, depending on how the filter is rotated.

However, the fundamental problem is a small bright thing in a large and much darker picture. That's not going to get exposed properly by the automatic algorithms in most cameras. One way or another, you have to expose so that the brightest part of the cat doesn't saturate the sensor. Yes, the surrounding scene will then seem darker, but this is quite fixable with non-linear brightening in post-processing. A logarithmic sloshing towards the bright end usually works well for scenes with high contrast, but only if the information was properly captured (the bright parts aren't blown).

There are several ways with most cameras to expose so that the bright parts aren't blown. You can use center spot metering, push the button partway with the cat in center (this freezes the exposure), then frame as desired and snap by pushing the button all the way. Some cameras have a mode that looks at many spots and exposes for the brightest. Or you can use the brute force method and just set the automatic exposure compensation to -2 or something. Just don't forget to set it back when you're done photographing the cat.