Actually, there are vet anesthesiologists but you don't see them at a general vet. At my vet there are 3 people doing dentals....one tech doing the dental, one tech monitoring vitals and the vet supervising and doing extractions if needed.
The larger specialty hospitals hire vet anesthesiologists. I don't know if the op has access to a teaching hospital, but they usually hire them.
There is a lot of great information about anesthesia at this link:
American College of Veterinary Anesthesia and Analgesia
and veterinary oral health here:
www.vohc.org