No.
It means she doesn't accept the fuss and bother that goes along with being the newest, most popular girl on the block.
I don't think the 'anti-' in 'anti-It girl' means, well, 'anti-' in the sense of opposed to or rebelling against something, in this case being the 'It girl'; I think it's closer in meaning to 'the antithesis of', whether this is the result of a conscious rebellion against sexual stereotyping or not.
Many of the celebrity anti-It girls in the past might indeed have been considered tomboys in their day, eg Diane Keaton in Annie Hall, Ally Sheedy in The Breakfast Club, or Amelia Earhart back in the 1920s (dubbed the 'anti-It girl' because she was the antithesis of her contemporary, the original It girl, Clara Bow), but they also expressed their individualism in other ways. Most significantly, they didn't dress or behave to please men, but to please themselves and, in doing so, they had a very different sexual allure to the frivolous sex goddesses of the day.
As for how best to define an anti-It girl, well, given what I've written above, the best I can come up with is 'the exact opposite of an It girl'.