My 7-year-old grand daughter is just starting to take lessons. She’s wanted to for a while, but simply didn’t have the coordination, strength or focus that made me comfortable about her doing more than a lead line pony ride. I certainly wouldn’t expect her to have the strength or self-possession to manage keeping a pony’s head up or handling ponytude. At the moment it’s still all unicorns and rainbows.
She’s also quite tall for her age, but 13.2 would be big for her.
If your daughter were mine, I’d be seeking out a more appropriate beginner pony that she can have fun on and gain lifelong confidence with. Doesn’t mean that this one is bad or mean, he’s just a bit sharp for her at her stage of riding, and would probably be happier in himself with a more mature rider.