If she wants to learn to read and she enjoys the lessons, I don't see you doing anything negative (seems positive to me). Teaching a willing learner is great.
Like it or not, kids who learn faster than >99% of other kids are just really different. They aren't the kinds of kids that teachers see every day or even every few years unless each teacher's class has a hundred kids (?). A teacher may base her view of development on the vast majority without knowing much about the <1%. This is how I try to envision a teacher's perspective.
A child who is ~3 who can read, say, a Bob Book, or do mental arithmetic without being taught is so different from others, a teacher may not have met more than one or two kids like her. And some of the kids here are past this level.
So, I can see that a teacher who hasn't been exposed to highly gifted kids could be skeptical or not understand the child. In a situation like this, I see nothing wrong with proving to her that your child is very bright, especially if you think your daughter needs something she isn't getting at (pre)school.
Please note that I am not advocating for frenzied test prep (FTP) here, nor do I think you are! FTP is not the same as teaching an enthusiastic little kid how to read (or, in the case of my kids, "how to wead.")
Val
