"Can I spin the hair from my pet?" is a frequently-asked question. Usually, pet hair is short, which makes it more difficult to spin, though in the past I have successfully blended very short dog hair with some longer sheep wool as a 'carrier'.
A friend brought over some amazing fur from her Alaskan malamutes. She had taken the softest fluff from the dogs' bellies and painstakingly removed the guard hairs. What was left looked like the softest, finest wool. Yes, short, but long enough to spin on its own (1-1.5 inches) and slightly crimpy. It's self-coloured white to dark grey. It looked as if it had come straight off a carder, and I suppose it had, the pet brush being very much like a small carder. (I bet that dog was in heaven having its belly brushed like that!)
After a little experimentation with different thicknesses and spinning methods, we had some extremely nice samples. The resulting yarn is quite fluffy, but in a soft fluffy way rather than hairy or scratchy. I'm sure that blending with wool would reduce this, but I quite like it and am curious about how a knitted garment would look. I've seen suggestions that the native Americans spun it, and I assume it's incredibly warm.