This certainly can be done. However, be sure that the physician you chose is an expert in lasers and that he/she has an array of lasers at their disposal. You do not want an inappropriate laser used in which the intensity or power is increased to compensate for an inexact wavelength. Some would even try to mistakenly erase a tattoo with an IPL. Q switched lasers (nd:Yag, Ruby, and Alexandrite) are superior for their short pulse duration and peak power.
Working around the eye is not a problem as long as a good eye shield is used.
There are a number of dermatologists and plastic surgeons who specialize in tattoo removal. I would seek one of them.