It would seem that beyond the formation of a country and the introduction of a new way of life to America, the Founding Fathers also introduced some pets.
George Washington and his family had many different breeds of dogs over their lifetimes. Washington had hounds imported from Britain, was gifted basset hounds from the Marquis de Lafayette, and would personally attend to the dogs when at his estate. Further, Washington would cross-breed his group of international pets to create the American Foxhound breed. He also bred mules.
After the war, Jefferson brought in Briards, a type of herding dog from France. He also kept a mockingbird and some bear cubs (the cubs spent time at the White House). John Adams and his wife kept dogs. Likely, all of them had horses at one point or another. I wonder what else they might have kept as pets.