It sounds like your daughter has quite a few issues going on that would prevent her from being able to run comfortably and without risking injury! Fortunately, as children grow into their bodies, they naturally learn how to more efficiently run and move their bodies, and the right style and brand of shoe can go a long way! However, you want to be sure that you start nipping problems in the bud, as soon as they arise. You certainly do not want her to develop a long term habit of running on her toes, as this could potentially cause some very bad injuries and pain down the road (if it has not already - in fact, her knee pain might completely be contributed to the mixture of toe running and over pronation that she is experiencing). My first piece of advice, before even focusing on shoes, is to seek out a running coach or running team for her to join, if possible. Connect her with professionals, elites, or just experienced runners who can help work with her on her form and teach her how to right her bad habits.

As far as shoes are concerned, many great brands that govern the adult running shoe market are also available in kids' sizes. Our article found here gives you a break down of some of the best running shoes for kids, as reviewed by our writers and shoe testers. Asics are always a great brand, especially for over pronators, because their thick-soled shoes (like the Asics Pre Contend 3 PS model on the list) offer extensive cushioning for the arch and a high ankle, to help stop the over pronating motion. The same is true for the Mizuno Wave Inspire 12s on the list, and the Asics Cumulus 18 GS. Basically, to help her with her over pronation and toe running, you first and foremost need a shoe that has supportive arches, a high and supportive ankle, and is wider with a thicker base. It would be a good idea, too, to encourage her to start thinking about her running stride: mainly, landing firmly on the ball of her foot, then transitioning her weight effortlessly to the heel, and then springing back up.

Sources:
https://runnerclick.com/best-running-shoes-for-kids-reviewed/