Good job keeping things positive and letting her have a good relationship with her dad!
I'm divorced because my ex serial cheated. We've been apart and co-parenting for about 4+ years and he always traveled before that, so I've always been the primary parent. We have 3 kids who are 9, 8, and 6. None of them have asked specifically why we are not together. Like you, I would not share that if they did. Maybe when they are much older they'll ask or figure it out, but no, that's not for kids to carry. They love their dad to pieces and he's great with them when he's around. So if they ask, I'll say we decided to get divorced. We're all much better this way...whatever.
As for how your daughter feels compared to everyone else...not to sound mean but, this is a bit falsified for drama on her part (not meaning that to sound harsh, but kids WILL emphasize stuff when they get focused on it). I'm quite sure none of the other kids are making her feel different in school in any way. I'm also shocked to hear EVERYONE else in her class/school has a happily married home-that's probably not the case and you could find examples to point out to her. In our school there are many single parents, widows, widowers, foster kids, kids being raised by grandparents..you name it. She is not in an odd situation at all, and her anxiety about it will pass. Tell her this is normal in lots of homes, and keep up the good work being positive!