I started playing guitar when I was your daughter’s age. I’ve studied music though did not get a music degree, and have played in bands since age 15. I have done a little bit of teaching.
You can start on any instrument (though see below about my daughter). Piano is a great instrument to start with, especially if she has the interest. You don’t have to work hard to get proper sounds out of it (compared to violin or clarinet, or even guitar, for example). Because a piano can play multiple notes, it’s a great solo or accompanying instrument. Learning piano develops a good foundation so that you could go to learn other instruments from there, if your interest changes. Drawbacks are purchase price, size (where do you put it), maintenance (needs professional tuning), and lack of portability. These are mitigated if you go electronic, though discuss with a teacher.
Anyone who goes on to a serious music career will have to learn piano, regardless of their primary instrument.
My son started learning the drums at age 7, now 8, because that’s what he was interested in. The drawback to drums is you don’t learn standard music notation, although he is learning drum notation.
My daughter is 10 and is interested in flute. The first teacher I talked to said he doesn’t teach kids until all their adult teeth are in because the embouchure changes too much. (I don’t know if this is a common viewpoint; I am going to look for another teacher, this has been on the back burner while she has been playing softball.)
Be aware that starting a child on an instrument is not just the music teacher’s job. You need to be a fully engaged participant. You don’t have to know the instrument but you do have to work with the teacher to understand expectations and help your child to be on a practice schedule that achieves weekly (usually) goals.
Bottom line is that your child will do best in the long if you encourage and nurture a natural interest, so if she’s thinking piano, think piano.