multiple locations is clearly plausible, probably more so than the alternative, given the fact that human settlements would have been isolated regularly. Nevertheless, surely it cant be ruled out that dogs could have accompanied the migration of humans. Animal domestication provides an interesting insight into the development of ancient humans. It also provides insights into the flexibility of wild animals. In modern times, last 100 years, quite a number of species have successfully adapted to urbanisation.
Evidence of horse domestication has potentially been pushed back to 9,000 years
BBC News - Saudis 'find evidence of early horse domestication'