From what I understood your SVG is made of a white object (the face) on a black background. Therefore we can not easily select the black eye as a separate object.
To overcome this a very fast method would be to use Inkscape's Bucket Fill tool (Shift + F7 ). By this we can create a new object outlining the shape of the undelying object we had applied it to. Colors and stroke properties will will be of our current defaults and needs to be adapted to match the source.
For more complex objects, or in case we need to obtain parts of a (foreground) object we can Break apart the existing path to create new objects.