DAKOTA Fanning turned down the role of the leukemia-stricken teen played by Sofia Vassilieva in “My Sister’s Keeper,” according to sources, because she “didn’t want to shave her head for the role.” Fanning, who’s filming “The Runaways” with Kristen Stewart and Riley Keough, might also have issues with Vassilieva’s co- star, Abigail Breslin. “SNL” once did a skit with Drew Barrymore and Amy Poehler mocking Fanning’s “jealousy” of Breslin’s Oscar nomination for “Little Miss Sunshine.”