Is it a good idea to let my pet have at least one litter?

No, there is no advantage to letting your pet have one litter. However there are plenty of advantages to having your pet spayed or neutered. These advantages include decreasing the chances of breast tumors later in life, decreasing the chance of cystic ovaries and uterine infections later in life, decreasing the desire to roam the neighborhood, decreasing the incidence of prostate cancer later in life, helping prevent spraying and marking, and also decreases the surplus of unwanted puppies and kittens.