We are not exactly told why Sandy moved to Florida. However, if you read between the lines of the story, it seems pretty clear that she moves because she is pregnant.
You can see this because of what is said in Chapter 12. There, Darry says "When Sandy went to Florida ... it wasn't Soda..." We don't know what "it" is, but I assume that "it" refers to who the baby's father was. That's why Soda was so devastated.
We can also infer that she was pregnant because Soda offerred to marry her before she left.
Remember that in these days (the book is from 1967) it was really quite shameful to get pregnant without being married. So it's realistic to think that someone would move if she got pregnant. And it's realistic to think that the guy would offer to marry her if he thought it was his.
One of the Curtis brothers in S. E. Hinton's novel, The Outsiders, Sodapop was in love with his girlfriend, Sandy. Apparently, Sandy becomes pregnant, and she moves to Florida to live with her grandparents. Soda proposes marriage to her, but Sandy turns him down (or gives him no answer). Soda writes to her during her stay in Florida, but the letters are returned unopened. It is implied that the baby is not Soda's, and that Sandy has been cheating on him. Sandy's parents probably sent her to Florida to either keep her away from the father and/or to keep her pregnancy a secret in Tulsa.