Moles and Skin Cancer?

I had a mole, looked suspicious to me, so I showed it to my GP and he said it was nothing. Its very small, way smaller than a pencil eraser head. But, its two colors. Or like two moles in one. Dark brown or black center and light brown around the edges. Its like the light color is forming out of the edges of the dark mole, but is round not irregular. He said to go to a dermatologist, and I did. she wasn't concerned and said to keep an eye one it. Every now and then I think about it, worried its melanoma. I am a red head, but i do not tan nor do i recall sunburns. also its in an area never exposed to the sun. its been at least 4 months and nothing changed, is that a good sign? She said she will do a biopsy if i want one, but she would recommend to watch it. what are your thoughts?