I would advise to first spin wool before moving to spinning dog hair, but there are people who started with spinning their dog's fur.
Here's the best page I've found so far about spinning dog hair: http://www.mdnpd.com/pd/default.htm
Your hair's already gathered, but when combing, its best to first brush with a rubber brush or a bristle brush to remove all the guard hairs then use an undercoat rake, slicker brush, or one of those fancy deshedder infomercial thingies (essentially an undercoat rake, but they work) to get the soft down fiber.
Dog hair can be dyed with the same acid dyes used to dye wool, and that includes food coloring/wilton's/koolaid. Just be aware that dye's transparent, so whatever color you dye the fiber will be "mixed" with the fiber's existing color. I personally prefer the natural color but if you do want to dye, I'd suggest you do it after spinning it into yarn since dog hair felts really easy