I thought the plan was to not domesticate the same animals, to help make this a bit different from the actual world.
This is why I added a couple of alternatives. Cormorant, capybara, ratites, even iguanas. Not to mention the three alternative carnivores skunk, polecat and mongoose.
Also, the distributions also sometimes lead to interesting results. Just consider that horses are only available in the new world and the old world only has elephants and dromedaries in terms of mounts.
In the end, you don't need to change everything in order to create something new. Replacing only cats/dogs with something else or horses with camels would already lead to a sufficiently different feel, even if there are goats, sheep and oxen.
One thing I want to mention though is that some animals are harder to domesticate and yet some harder-to-domesticate animals have been domesticated in the real world while others have not, or at least not as much. Maybe some sort of "luck" factor should be involved when attempting domestication. For example, horses have been domesticated in asia. In north america, however, the remaining horses were hunted to extinction. Similarly, emus were never domesticated in australia while the aurochs was in europe, despite the aurochs being meaner and harder to tame than emus.
Edit:
One thing to consider: The invention of the (cart) wheel has been attributed to the presence of draft animals. The americas, for instance, which lacked domesticated bovines and equines never got to invent the wheel, because humans move weight more efficiently by carrying it, rather than pulling it. And llamas were used primarily by mountain societies, which hindered the usage of wheels. Same for the dromedary, which was mostly used in sandy areas. Carrying stuff on the animal's back was easier.
