When repainting any 13 year old walls, primer is an absolute neccessity especially since you're going over flat paint. The flat paint will consume the sheen of the paint if you paint it without primer. Prime all areas for professional results and apply two full coats of quality acrylic paint.

Michael

Thanks Michael! Do I use anything on the spot or just paint?

I would sand or clean the area before painting. I don't see why Kilz would be needed. Kilz is really a stain killer and though the area may be dirty from the dog, it probably isn't a stain that will bleed through the latex paint.