Probably everybody, who saw in the film "I Am Legend" (2007) Will Smith walking though New York with his German Shepherd "Sam" as his last and only friend, was reminded of a very similar scene in the "The Road Warrior" (1981) with Mel Gibson.
Without any doubt the image of a man and his dog is already an icon and has older role models:
Dogs are good companions faithful and most loyal to their masters, so that they are even called sometimes "the oldest friend of man". Maybe here’s the root for their popularity in post apocalyptic movies. If they are the oldest friends maybe they should also be the last ones.
Two more examples of dogs in post apocalyptic movies :
A Boy and His Dog (1975) - maybe this was the inspiration for Mad Max.
Downstream (maybe next year)
House of Cards
2 days ago