Anesthesia and toddlers...?!

You have little to worry about. Anesthesiologist are among the most highly trained physicians around.

I got this from wikipedia, have a look:

Anesthesiologists are the most extensively-trained anesthesia providers in the United States. Anesthesiologists are physicians (MD or DO) who have chosen to specialize in anesthesiology. Anesthesiologists in the United States must have completed an undergraduate college degree, including pre-medical requirements. Like other physicians, anesthesiologists complete four years of medical school. Physician training programs in the United States, without exception, require four years of residency training for board certification eligibility in the specialty of anesthesiology. An anesthesiology residency requires a one year medical or surgical internship followed by three years of anesthesiology training.
Anesthesiology residency training in the U.S. encompasses the full scope of perioperative medicine, including pre-operative medical evaluation, management of pre-existing disease in the surgical patient, intraoperative life support, intraoperative pain control, post-operative recovery, intensive care medicine, and chronic and acute pain management. After residency, many anesthesiologists complete an additional fellowship year of subspecialty training in areas such as pain management, cardiac anesthesiology, pediatric anesthesiology, neuro anesthesiology, obstetric anesthesiology or critical care medicine.

If anything goes wrong, they know exactly what to do.

Btw, my little guy had his adenoids removed two weeks ago. Surgery was on a Friday, was back in school on Monday. The only after-effect he had was his temperature fluctuated a bit for a few days, but that was just due to the anesthetic.