I am all about intrinsic rewards, but I want to know how she is progressing. I think if she had a decent school teacher last year...and this year...she would be fluently reading everything in sight. I think if she would let me (and I won't push it) I could teach her a year's worth of reading in about 2 weeks. That's how ready ability-wise I think she is.
I remember when my kids were that age, especially my first (who is also my EG kiddo). I could see how high his ability was and sometimes got frustrated when I didn't see it in what he was actually interested in and doing at the time. I got frustrated with his preschool sometimes and wondered if I'd made the right choice; we had him in a Montessori totally-student-led type learning environment and he didn't ever show the slightest interest in learning how to read etc. I felt like he was sooo so ready, I hated that I couldn't get him into regular K already (our district just doesn't do early entrance no matter what), I felt like he could do and be so much more! But really, really, the best thing ever was just to read to him. Read your dd the "big" books she's interested in, but don't make it about learning to read on her own unless she is showing you she wants to and she's doing the leading. My ds didn't learn how to read before K, but by the end of K, on his own, without any help from school really (and definitely not from us leading him at home)... he was reading soooo so far above grade level. It happens when it happens, when the child is ready for it to happen.
Another person mentioned their child hiding their reading ability because they were afraid their parents might stop reading to them - that happened with our ds too - we only found out he knew how to read because he accidentally read to his aunt when we visited during the winter holiday.
The years when they are young and really love to be read to pass by so quickly. The years where you'll be navigating how to get your child the advancement they need etc will come quickly enough. Having a high ability child is a blessing and it's a ton of fun, but it doesn't have to be a race to see who reads first and fastest, or who does anything academic first and fastest. When our kids are racing, we need to be there to support them, but we don't need to push them. They'll develop their own inner "push".
Best wishes,
polarbear