Been taking our nine year old grandson karting for a couple of years now along with his other grandad. Remarkably cheap. We got him a used Energy chassis with some spares for around $2k. The Monster 206 engine is awesome, other than oil changes, and making sure it's got the right slide in it for his age group, it requires zero maintenance. Super cheap to run, we've probably done 12-15 days and including one set of tires, and money to have the frame professionally straightened after a crash, we've probably spent less than $1,000 in parts and consumables.
One thing, he's only done one actual race day. We started doing test days the first year, after which he was enjoying it, so for the next year, we decided once he felt ready he'd race. After a couple of test days, we entered a race at his request. While it was a good day and he enjoyed it, unfortunately, he had a pretty big hit with a girl in his class. Both karts were bent to the point of the frame scraping on the ground and at least one wheel was in the air. We got the chassis repaired and ready for this year, but his confidence took a hit and he wants to go back to test days only.
Our local track (East Lancing Kart Track) in southern Michigan is great. They are open from early April to late October. Two local track races (Sundays) per month, on that Saturday there's another smaller group who race and open practice for all other sessions (still easily four sessions per day). On the off weekends, it's open practice Sat and Sun.
I'd let your daughter try a few test sessions before racing. Our motto is he has to want to go. We will never force him. He gets to go at his own pace, with no criticism, just coaching and suggestions. None of us expect the next Max or Lewis, we just want him to have fun.
A few other parents/grandparents ask about the risk. Honestly, I don't see it as much of a risk. His main sport is football, he also rides horses and skis. All three of those are far more dangerous than motorsport, but no one bats an eye at those sports.
