Well a Google search finds Taxonomy Database with Breeds, which appears to do breeds for sheep, dog, swine, cattle, goat and horse.
However since breed is a rather vague term (Wikipedia), and breeds are usually defined by national pedigree authorities. For example in the UK dog breeds are defined by The Kennel Club, in the USA they are defined by the American Kennel Club, other countries have their own authorities (see Wikipedia), and they do not always agree on the naming or definition of their breeds. Since a taxonomy, like any classification or ontology, is intended to ensure that we are all talking about the same thing all these conflicting definitions make things complicated.
I suspect that the taxonomic authorities (Wikipedia) have looked into trying to sort all this out and deal with the other sub-subspecies distinctions (e.g. ecotype, cultivar, form, morph, etc.) and have decided to defer looking at it until they have time and the need is pressing.
Of course this has consequences for the bioinformatics databases, since these distinctions are lost. One case that comes to mind is the Arabidopsis thaliana genome where two different ecotypes were sequenced (Landsberg erecta and Columbia), due to the restrictions of the NCBI Taxonomy it is not possible to distinguish these in the sequence databases. Being able to distinguish would be useful since genetic mapping in Arabidopsis used a set of lines derived from crosses between these two ecotypes (see "How to map using the RI lines") and thus mapping markers from the genetic maps on to the genome sequence requires knowledge of which is which. Of course projects such as 1001 genomes are dealing with this as well as harvesting more sequence variation data.