It could be an impression of your dog. Every living thing leaves a little energy behind throughout the day. Sometimes, when that living thing is habitual and does the same things over and over in the same places, the energy accumulates and creates an impression. If this other dog does not interact with you or notice that you are there, and it is doing what your dog does, than it is probably an impression. Simply cleansing the house will get rid of it.
They don't always look identical. It's similar to a thoughtform in that it takes the shape of what the energy's owner sees themselves to be. It is probably missing a yellow spot and seems lighter because a dog's color spectrum is different than ours. Some people say they see in black and white, but I don't think that is true. I think the colors they see are just different. My chihuahua likes pink and purple (all shades). Anything with either of those colors, he automatically takes a liking to and claims as his own. Don't ask me why! But it proves to me he isn't colorblind.
I'm usually very good with keeping on top of cleansing my house. But when I go out, I see, feel, and hear impressions all the time. You can tell the difference between them and a spirit messing with you, when you can't sense a presence, but instead feel the lingering energy of someone, just as you would on the possessions of an individual.