Your daughter sounds a lot (maybe even eerily so) like my daughter would have been described by me (at age 3-5 or so). Barring being quick to cry, that is. DD (now 16) has always had extraordinary emotional regulation and maturity.
It sounds like your little one has some significant asynchrony happening there, though-- it's not unusual, do know that. MANY 5-7yo children who are highly observant or gifted still tend to be pretty prone to meltdowns from being overwhelmed.
Honestly, the only thing that I wish that I'd known a LOT more about at that point was to keep a close eye on the perfectionism and do whatever I could to nip that in the bud. Press on it with activities that are:
a) ungraded, open-ended, with NO "right" answer, and no percentages or grades attached, and
b) things that she does NOT find instantly easy-- but finds that her performance is roughly equal to her effort.
Keep an eye on how rapidly she learns. That is the key thing that (IME) separates garden-variety gifted from higher levels, and it ultimately determines just how specialized or unusual a child's educational needs are or become.
Your description of her reading arc, for example, would lead me to suspect that she's probably MG, but could be HG (which formal settings don't handle all that well).
The Goldilocks thing with math, though- oy. That sure sounds familiar. If it isn't instant, it's "too hard." If it is instant, then it's not hard enough. Ugh. My best been there advice is that such children-- particularly if they are extremely capable-- may need to be specifically taught how to fail and learn from failure as part of the learning process. This is true of children that avoid occasions where failure is a distinct possibility. It's very easy for homeschooled-- particularly unschooled-- children to mask that this is precisely what they are doing when they "lead" the child-led process by avoiding things that they aren't good at already by just... not... choosing to do those things.
Yes, that is something to keep an eye on. I've no idea if it is truly unique to gifted children, but it does seem to be close to universal among that cohort, anyway.
