LE never said much about the dog. It was a Queensland Heeler named "Blue." I assume police brought it back to the extended family, but I don't think I ever heard them publicly confirm that. Heelers live about 13-15 years according to Wikipedia, so it's certainly no longer alive now.
BTW, the fact that it was a Heeler makes me all the more confident that Fisher fled the area in a way that precluded Blue from following. Heelers have a strong herding instinct; if you don't give them a job, they'll find one. I suppose it's possible that a really well-attuned dog could have sensed from sounds/smells that Fisher was dangerously angry and not worth following. But I think the far more likely explanation is that it stuck to the area around the car because that was all it had as a familiar frame of reference.
Back to the case more generally, to the best of my recollection, police have only publicly acknowledged two leads beyond the vehicle/dog scene: (1) one of the LE people interviewed in the documentary says that there were credible sightings of him in Gila County in the days immediately after the murders, and (2) Detective Kirkham said in 2002 that he believed Fisher may have called the
America's Most Wanted tipline in August 2001 (
link to news story). Kirkham died after a stroke in 2006 (
source). Kirkham supposedly told several people before he died that believed Fisher would be found in Mexico or Latin America.
I do wish that police would say more about what leads them to the conclusion that he's alive. I understand that they have good reason to not discuss specific leads or evidence, but a general statement like "We have evidence which leads us to beleive that Fisher fled the country" or "we have evidence that Fisher planned to escape" would I think help to keep up public interest in the case and counter the theory that he committed suicide in Gila County.