There is a dark grey irregular shaped spot on the white portion of my baby girl's eyeball (8 months old), what's that? Is it going to go away later?

Normal. Many people brown or gray spots on the white part of the eye called the sclera. It is pretty common. This is scleral melanocytosis. It is not harmful and treatment is usually considered cosmetic.
Could be fine. Nearly everyone has pigments in their skin, and even in the white of the eye. Often these deposits of pigment are normal. On the skin they are seen as freckles and such. A grey spot on the white of the eye, then, could be such a normal finding. But i would recommend seeing your pediatrician to see if it is this innocent finding or not.