Good question. As an inspector, I can tell you we only check for a valid license, and I don't recall whether or not learner's permits are OK. Having said that, I do remember that a minor was permitted to drive a school-built "vehicle" on the 130MPH course, either last year or the year before. I can't remember whether or not the young driver had any kind of license. They were from somewhere in Washington. However, they may have been limited to the (much shorter) barstool course. As I recall, they made their speed goal, which was something like 20 or 30 MPH.
The rules specify no age limit, and only require "...current valid state drivers license...". However, they also require that competitors "...sign a loss damage waiver...". So, if your daughter is a minor, her signature on the waiver may not be valid. Also, if her learner's permit requires that a parent/guardian/adult be with her when driving, then she'd be out as passengers are prohibited.
So, I'd suggest you contact Ellen at usfra@saltflats.com, or 801-485-2262, or 801-583-3765. She answers questions promptly, and I suspect she'll know the answer. If not, she'll contact somebody who does know. I hope we'll see you both in September!!!
Jeff