I was also a daydreamer and a reader, but this is just my personal experience, so YMMV.
When I was in second and third grade, I was in a mixed classroom (one room schoolhouse type) and I loved it. I finished my work quickly and I could listen to the lessons for the upper grades. Then halfway through 3rd grade, we moved to a different state where the curriculum was focused on test preparation and repetition. I was extremely bored and complained loudly to my parents every day. They got me tested by someone at the school, not sure which test, but I remember being very stressed out and worried, overthinking which answers would prove that I was smart enough. I was desperate for something more challenging. I'm not sure exactly what the test results were, or what my parents told me, but the school refused to do anything, and the messages I internalized were "you're not good enough," "your needs don't matter," and "you'll just have to figure it out on your own." Having your parents give up when you want more, but don't quite meet the cutoff, is an awful place to be, in my experience.
The things I began to believe about myself back then plague me still. There were other times when my parents probably could have changed things for the better (I spent all of 8th grade in remedial classes due to being the new kid with no records and I'm sure my parents had no idea). But I thought I had to accept the way things were, that for some reason, my needs weren't credible or valid. I'm sure my parents didn't intend for all of that to happen, but I wish they'd trusted me more, been more proactive the one time I spoke up, because I never did again.
I would talk to your daughter, ask her what she wants. But I would convey your absolute faith in her that she could do the higher level work and that you are willing to advocate for her if she thought she would enjoy the gifted program. I think it is so important for her to know that she has a right to honestly speak up for her needs, and that even if it doesn't work out this time, you will continue to listen to her, find other options, and advocate for her until she can do it for herself.
If it's what your daughter wants, my vote is definitely push.
