I'm not exactly sure but my best friend is a hair stylist and owner of a hair salon. I asked her this same question because my daughter also has curly hair and we have been experiencing the same thing. She advised me to wait as long as possible before cutting it if we wanted to keep the curls. She said the longer you wait to cut it, the curlier it will stay. You may be ok, though if you just take a tiny bit off.
Right now our daughter is sporting a real baby mullet. We have been putting it in pigtails to keep the hair out of her eyes and to keep the mullet look away. Her hair is sooooo curly right after a bath, even on top. After she sleeps on it, though, it softens up and looks like what you describe. A little water or detangler helps the curls spring back and tames the mullet look. The ringlets also make her hair look a whole lot shorter than it really is.
If you do decide to cut her hair, I would strongly recommend having a professional do it. There are a lot of fun, kid-focused hair places that specialize in first haircuts.They might be able to give you good advice on how to cut it, what her hair type is (or could be) and what to expect in the future with her curls.
Good luck!