As George said, it's really so many variables that it's hard to know. It sounds like all of the readiness pieces are
there-- but the ability to meld them together and decode/comprehend is a different kind of cognitive task, IME.
DD never really did that on her own. I think that she wasn't sure what the "magic" step was, and so she assumed that there was more to "reading" than there really was-- so she never took it on her own.
She stayed at about the level you describe for
two years.She was starting to use whole language (sight memorization) instead of "decoding" phonetically, and my mom (an elementary reading specialist with severe dyslexia) told us to intervene and teach her decoding instead. So we did, using leveled readers.
It took about four sessions, I think. She almost immediately transitioned to hours of sustained silent reading, jumped reading levels at a rate that boggled the mind (still does, really)-- she went from BOB books to Harry Potter in about six months. Not sure-- it was less than that, probably, because I only found out about the Harry Potter because it disappeared from the shelf and I found her with it late one night in her bed. She's voracious and has plowed her way through thousands of books in the 10+ years since. She went from "not really reading yet" to at least a middle school level of reading proficiency and speed within a few months.
She was, early on in that period, polishing off books like MTH and Cam Jansen at a rate of one every couple of
hours. She was five then, but had been taught with those phonetically controlled readers for a couple of weeks while she was still four.
It's really, really hard for me to say how long it would have taken her if we'd done nothing at all. I simply don't know. I do know that it opened an entire world of joy for her, and I can't really think why we didn't do it sooner, honestly. Reading has given her an enormous positive method of coping with being so different, an escape from her worries and troubles, etc. I have exactly zero regrets that she didn't learn to read "in school" with most other children. It made OUR lives easier, too, because it was a quiet and unobtrusive way to keep her brain "fed" in almost any situation, with most outsiders being none the wiser.
ETA: The other thing about reading independently is that it gives the child a level of autonomy and agency that they otherwise lack. That is, if it's print, THEY can decide whether to access it for themselves. That's very powerful for some children, and my DD was one of them. She no longer needed to find an adult to provide her with stories from books, ask permission to read, etc. It was HERS.
