Another vote for the SL1. A fun camera to carry around and gives you all the flexibility of interchangeable lenses. And the price - especially for refurbished - is a deal hard to pass up! (I should know - I bought one refurbished a few months ago)!
Of course, if possible, I would take her to a camera store and try out a few cameras and see what she likes. That answer will be far more important than what we recommend.
+1 Refurbished SL1's are a terrific value, a very capable little camera for less than the much more limited SX60.
As dak723 suggested, she should go to a camera store and try out a variety of cameras see how the various options handle and if the size and controls are what she is looking for. If the SL1 is too small, a used Rebel T3i, T4i or T5i (600D-700D) have roughly the same sensor and image quality in a somewhat larger body.
The SX60's sensor is a relatively tiny 6.17x4.55mm, just a little larger than a smart phone sensor. The SL1 and the Rebel's listed above have a sensor that is over 10x larger by area (22.30x14.90mm) that will produce much higher quality images and enable greater artistic creativity with ability to control depth of field and shoot effectively in low light. The manual controls on these cameras will be a great learning tool for a young, learning photographer. The ability to change lenses will allow her to buy or borrow a wide variety of excellent Canon lenses to open up new doors artistic expression. Sure the SX60 has a huge zoom range, but that might be its only real advantage over a Rebel DSLR.
Here is a link that discusses digital camera sensor sizes and a comparative chart for reference.
Here is another link to compare camera sizes. Note the SL1 body is pretty similar in size to the SX60. With a 18-55 STM lens attached, the SL1 is over an inch deeper, but with the new EF-S 24mm f/2.8 STM lens, the SL1 is smaller and lighter. http://camerasize.com/compact/#385,448.377,448.439,449.377,ha,thttp://camerasize.com/compact/#385,448.377,448.439,449.377,ha,f