There is always more than one way to do it. And one way to tackle 'hard' problems is to break them in bits that are only just beyond what you can do know, and learn how to do them.
My line of approach would be to build something using just the keyboard [space bar] to both start and stop a 'stopwatch' in the first instance. If you were doing it in Python, read the time when the space bar is first pressed, and again when it is pressed a second time. Work out and display the difference and you have your daughter's performance. You've already got something that 'works'! Well done!
For the 'magic beam' part - how about an ultrasonic sensor - like a reversing aid on a car? If you google for 'Pi' + 'ultrasonic sensor' you'll find several existing examples of how to implement this. Instead of measuring distance, perhaps you just want to look for a sudden reduction in distance as your runner causes a reflection of the beam? When you see that you just use it as an alternative to the second 'stopwatch' keypress. Job done!
How To Ask Questions The Smart Way: http://www.catb.org/~esr/faqs/smart-questions.html
How to Report Bugs Effectively: http://www.chiark.greenend.org.uk/~sgtatham/bugs.html