As is my wont, I googled the term to show her a picture. I was chagrined to find that everything connected to the term "dog run" had to do with kennels and chain-link fences. It wasn't until I added the word porch to the search that I was finally able to get the proper hits.
From the Handbook of Texas Online: "DOG-RUN HOUSES. The dog-run, dog-trot, or double log cabin was a common type of house in Texas at the middle of the nineteenth century. The building consisted of two cabins separated by a ten or fifteen foot passageway, with a continuous gabled roof covering both cabins and the passageway between them, or dog-run...."