I would start with a dermatologist. I say this not just because I am one, but because I feel that the extensive training and experience we possess makes us experts in evaluating and treating pigmented lesions. It may be that your "mole" is not a mole at all but another lesion like a seborrheic keratosis or a hemangioma. It may be treated with cryotherapy (freezing) or scraped off rather than excised, leaving you with a better looking result and a somewhat fuller wallet. If your dermatolgist feels that you would be better served by a plastic surgeon, a referral would certainly be forthcoming.
Not only would a dermatolgist examine the mole you are concerned about, but we would also embark on a full skin exam.
Many of us perform dermatoscoppy which increases the proper diagnosis of suspicious lesions from a 65% accuracy rate with the naked eye to an 85% rate with a dermoscopy. Personally, this little epilumenscent light, has saved many of my patients from a biopsy.
I feel that most plastic surgeons, if they had a relative with a suspicious lesion would send them to a dermatologist instead of one of their colleagues, the same way I would consult a plastic surgeon if my eyebrows begin to cover my eyes.