The answer to your question (which is not strange at all, BTW) is - absolutely!
Dog fur can make wonderful yarn. Some kinds can be used to mimic more expensive fibers, like angora or mohair. But the nice thing about dog fur is it's a whole lot cheaper
Here are a few things to consider:
- Dog fur is almost always really warm. So you probably wouldn't want to use it for a warm-weather item. But it would be great in a hat or gloves (or other item) for someone who is outside a lot in the winter.
- It usually isn't very elastic, so a lot of people like to mix it with a fiber that is - like wool. But it can also be spun by itself. If you do that, you just have to take the lack of elasticity into consideration when you're knitting with it.
- Even though the animal may have long hair, the fur may not be that long. Remember to check the length of the individual hairs - the staple length - so you'll know how to prepare and spin it. And if you find that the length varies it's probably a good idea to try to keep fibers of the same length together; they'll spin better that way and the finished yarn will have less chance of pilling.
- There may be some not-so-soft hairs mixed in with the soft stuff. I'm no dog expert, but I do know that some have more than one coat. There may be an outer coat that is usually coarser (because its main purpose is protection from the weather) and an inner coat that is finer (because its main purpose is to keep the animal warm). If the dog has two coats and is shedding it tends to be the undercoat that comes off. But if all the fur is being removed - ie with clipping - you'd get both coats. Since you're clipping - or shaving - you might have to remove some coarser hairs. Or maybe not - as I said, it depends on the dog.
The thing about dog fur is that the amounts can be deceptive. You say your dog is small, but I'll bet you find that you will soon have a lot more fiber to deal with than you planned on!
I just joined and this is my first post here, so you'll probably get other answers that will give you more information. But I hope that helps get you started. Have fun!