Best Doctor for Mole Removal on the Eyelash Area?

While many types of physicians could safely remove this lesion with minimal scarring, you would be well served in visiting a dermatologist. Dermatologists are the experts on skin, hair, and nails, and routinely perform this type of medical service every day.
This lesion could likely be removed from the lid with minimal scarring, depending on the size of its base (how much is actually attached at the base to the eyelid). It's a bit difficult to tell from the angle of the photo, but the base of the lesion may involve the eyelashes. In this case, it would be best to shave the lesion so the eyelashes have the best chance to regrow without removing their roots. You would have a small scar, though...there's no way around that.

That mole need a lot of expertise in eye lid surgery and anatomy.
See a plastic surgeon, The concern is having a bald area in the lash line.
Therefore a wedge resction is the procedure of choice to prevent a bald area.