In Texas (at least everywhere I’ve gotten a ticket) you have the option to take defensive driving and the ticket isn’t charged on your record (or therefor increase your insurance rates). It’s still there, but it’s excused. Essentially you plead “No Contest” to the charge, sign up and take the course within an allotted time, and get the certificate of completion to the court in a timely manner. The ticket then doesn’t count against your record. You can do it all by mail.
The course is available online, in person, with a comedian teaching it, just about any way you want. Typically I’ve paid 20–30 bucks and it takes most of the day (6–8 hours I want to say).
You get one of these “get out of jail free” options a year. It should be on the back of your ticket or on an additional piece of paper the officer gave your daughter.
What @robmandu mentions about negotiating a period of good behavior is called deferred adjudication I believe. You’re put on probation for a certain period and if you make it through, the charges are dismissed. The downside being if you don’t make it through the period, both charges (the one you’re on probation for, and the new one) go through without a shot at your other options typically. I’m sure that’s negotiable as well, but judges generally don’t like it when you screw up on probation. For someone who just started driving, it may not be a good bet.