I just received as a birthday present, a book called "Fleece Dogs", which tells you how to do just this -- use dog fur (w/ or w/o sheep wool) to replicate your dog. It looks really cool and I'd love to try it!
That's the book that inspired me to needle felt! I had never heard of needle felting before coming across Fleece Dogs by accident in a bookstore.
Here is a pic of my very first needle felted dog. It took me only 2 hours, but I have progressed somewhat since then! That was almost 2 years ago now, and my sculptures take me more like 12 hours and are more firmly felted.
I've become more obsessed with detail.