Wish her all the best, and regretfully start the hiring process over again. Either she's as good as she thinks she is, and will quickly find a better job at a better salary, or she's making a big mistake that she will soon regret, but either way she's made her decision, and you'd be wisest to let her stick with it. From this moment forward, all her decisions are hers to own, they aren't your problem anymore.
If this becomes a pattern, then you aren't as competitive an employer in today's market as you thought you were. (Maybe it's not salary --maybe this is an unappealing workplace for some other reason?) Short of that, you have to chalk it up to the unpredictability of individual human beings.
A final thought: As noted by @elrobis in the comments, in some industries, notably IT, it's increasingly common for ambitious young employees to job-hop frequently. It's often be considerably easier and quicker for a competent junior programmer to get raises and promotions by moving from company to company than by staying in one place. It would probably have been smarter of her to have secured the next job before quitting this one, but again, that isn't your problem any more.