I think you are absolutely right to see that teaching her resilience is the key here. And you're absolutely right that it's good to encourage her to be her sensitive and caring self. At least until she's getting flattened on a regular basis by the steamroller of the tween years.
She's getting to an age where the drama will increase in some of her classmates, and in the next few years, she's going to be presented with even more challenges. Wanting to be liked can lead to an unwillingness to say "no" to unhealthy offers - drugs, sex, booze. And your daughter, right now, is unable to say "no" to an unhealthy offer of fake friendship. She thinks that walking away from this girl is a poor reflection on her own self.
You ask how you can help her. I think, after a year of this, it's time to say, "You know what? I cannot help her myself." There's no shame in that. You send her to a public school because you cannot teach her the subjects they do. You send her to the doctor because you cannot diagnose strep throat or check for scoliosis or (one of these days) do a pelvic exam. You don't clean her teeth or give her dental x-rays. That's not a put-down of you, right? Nor of her. It means that those are not areas of expertise for you or for her. Find a therapist, either through your insurance company or your pediatrician or through referrals from others, and then talk to that professional beforehand to learn ways to present this to your daughter.
From your end, as mom, you can remind your daughter that, when classmate Adam says that Nigeria is in South America, she's knows it's not true. If Adam can learn the truth, great. But if he can't, it's not a reflection on her. She can ignore it and move on. If Sally says that 4 plus 6 equals 17, and can't be talked out of it, your daughter can move on. If Sally and Adam share their views with 10 other kids and say that your daughter is an idiot for not seeing it that way, she can (and must) move on. So if other kids are talking behind her back (and we don't know how much they are, because you say "allegedly"), your daughter needs the skills to walk away from that and not feel that someone's desire to hurt her is necessarily indicative of how others feel, and not a reflection of the truth anyway. A good therapist, who will also help you find additional ways to be supportive, can help your daughter walk away from the "4 + 6 = 17" crowd without feeling she's missing much. And, while it's good that she does have a friend, it's going to be important for her to find friends who meet her needs and not just those who seek out her undivided attention.
Two mantras for your daughter:
1) You don't have to go to every fight you're invited to.
2) As flight attendants say, you put the oxygen mask on yourself first before attending to the needs of others. Otherwise, nobody's getting enough air.