Best Doctor for Mole Removal on the Eyelash Area?

This mole is relatively straightforward to remove and requires only local anesthesia.  I would recommend that your physician have it evaluated as a specimen by a pathologist. 

I recommend seeing a board certified plastic surgeon for this lesion.  It's important to preserve the hair along the area and to achieve as best as possible cosmetic results.

You should see a board certified plastic surgeon. The concern with lesions on the eyelid margin is twofold. First, to preserve the eyelashes to the extent possible and second, how to achieve anesthesia in this delicate area. I commonly recommend some oral or intravenous sedation to try to achieve the best cosmetic result and surgical experience in this area. I recommend that you find a surgeon with experience in the eyelid region who will not minimize the risks and benefits of the procedure. Best of luck to you.

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.