There aren't many books about horse breeding suitable for children, but I would recommend "Blessed Are the Brood Mares" and "Blessed Are the Foals" first. "Breeding Horses" by Davies-Morel would also be interesting, though it might be too technical for your daughter; enough reproductive physiology of the mare and stallion is included to clarify the management techniques which are explained later in the book, but unnecessary details are avoided.
I will owl you information about various breeds to consider, along with information regarding upcoming horse shows.