Just to poke my nose in here.
You started of by saying that what constitutes a dog is that it can only mate with other dogs.
This is actually inaccurate (at least as far as dogs go). Fertile hybrids of dogs and other species of canids are relatively common. Dog-wolf, dog-coyote, even dog-fox hybrids are known. The simplified explanation is that the divergence (speciation events) separating the various species were relatively (evolutionarily speaking) recent, and total genetic isolation has not been achieved. Often the F2 generation of these hybrids "breeds back" to the "wild type".
NosyQ