Get a level 2 reader. Tell her if she wants to stay up past her bedtime she can stay up late to read. When my son tries a challenging book he only reads a page or two before he gets tired. Books on his level he can read anywhere from a few pages to the whole book in one sitting. Alternate which level book you offer. I'm not sure how the leveled readers match but from my limited experience my son reads level 2 chapter books and grade 1.5 books so I think they're the same level. Example Fly Guy and Goodnight Moon are grade 1.5 and The Magic Set and Henry and Mudge are level 2. Those are books he can read as much as he wants to which is usually a lot more when he can stay up late reading.
The Tale of Benjamin Bunny is grade level 3.5 and Maximum Boy is grade level 3.7. That's two books he's struggling through. That means he can only read one page or two pages and it literally makes him tired. He'll still gladly try it if it means he can stay up late reading. But then he doesn't stay up late he gets tired and goes to sleep.
That getting to read past bedtime really got my kid past the hump from "being able to read" to actually reading. And actively reading has recently lead to an interesting part in the book where he kept reading because it was a very interesting part. That's the first time he's done that so I think he's transitioning to where the decoding's automatic enough for him to start enjoying the story. We're on the cusp between reader and fluent reader. You're on the cusp between emergent reader and reader. The part that works to get past both "humps" is to offer to let them read past bedtime, it's the one time of day with a built in motivation.
Scholastic book wizard (google it) lets you know the level of many books.
