I wouldn't go on early milestones to predict giftedness. Not all gifted kids talk, walk or read early. My PG son did none of these things - though once he started school in April he got to reading magic treehouse by November. He could do maths preschool but we weren't talking amazing earth dropping stuff. I would never have got him tested without pressure from a friend.
She sounds almost exactly like my son, honestly. We started practicing reading, on his request, when he was just shy of 5. He picked up blending easily, we did Progressive Phonics books and he read the "red words" without problems. But actual, fluent reading just kind of popped up this May. Let's see...my May 21st journal entry from this year (so 6 years 7 months) says "He's reading now...picking up books and asking for help with only one word in 20." My July 13th entry is about how he plowed through his first chapter book, a Magic Treehouse, in one sitting. He now reads on about a 3rd-4th grade level, we're going to work through Charlotte's Web together this week.
He's been adding fluently about the same amount of time, but a couple of months ago he seemed frustrated about subtraction so we worked on it and now it's pretty fluent. And he's gotten really good at skip-counting, to where he asked me the other night how many seconds are in 40 minutes, and I explained how to get the answer, and he did the heavy lifting himself. He also did some exercises on division by equal groups, and with just a bit of trial and error got answers like 36/6 correct. It's fun stuff to see them making connections!
A few things, though, make me hesitate to assume that my son is gifted or even high IQ. One is the reports of profoundly gifted kids' parents here. My kids are NOT on that level! Another is our pediatrician who said, when my son was an infant, that early verbal skill is the best predictor of high IQ. My son was on the late end for talking, and I guess I internalized the pediatrician's comment because I've pretty much scrubbed him mentally from Team Gifted. Another factor is my daughter. She is crazily bright. At 4.5 she's reading fluently at a ~2nd grade level, adding and subtracting with great number sense, etc. Crazy kid just listened to an audiobook version of Robinson Crusoe today, and reported back on the content with great comprehension. *She* might be gifted, we'll have to see how she continues to progress. Jury's definitely still out on my son. If we had a chance to be tracked into a gifted program, I would not be attached to getting him in. I might think differently about her.
Educational choice is so overwhelming and complicated! How could you *not* want the very best for your kids, right?!
I forgot to answer the question. To me the answer in this case is NO. While on the whole I think refusing to do things against your ethics is right (and it has caused me a lot of difficulty) I don't think you should inflict your ethics in your daughter. A medical system where only the rich receive proper treatment is unethical but if you can by all means you should take your child to the doctor.
If you see an ethical problem then you should work on fixing it not your daughter who isn't old enough to see the problem.
Does that help?