It sounds like psoriasis. My daughter had it at 4 years. It is rare to get ringworm on the scalp. Usually it is a hand or something as you can get ringworm from cats so it shows up where you touch the animal at. You can take her to a regular doctor first and get his recommendation. My daughter is now 14. She uses a tar shampoo (which smells exactly what it sounds like). Neutragena has a nice one.
Psoriasis you can look up online - especially in the scalp and in children to see if the scales (the name for what you are seeing) are the same. It really does not bother them and if it is psoriasis you may also see it on her elbows, knees, eyelids in the future. The medications that are out there for psoriasis are very strong and most are given only to adults.
One of the treatments is making sure to get enough UV rays. But this will be something that is lifelong, unfortunately, not something that goes away and it is not harmful, not contagious, winter months are usually the worse as she will be inside more. You are welcome to contact me offline.