I would rent one that fits her as much as possible to see how she likes it. Then if she really wants to continue you could purchase one.
I begged for piano lessons when I was a kid. I went out into the garage several days per week and uncovered the piano and picked on it. I even wrote the whole alphabet, then repeated it as far as I could, on the keys so I could remember what notes were what.
My mom said "I paid for piano lessons for your brother and then your sister and had to fight with them every day to get them to practice. I'm not going through that with you!"
In 5th grade we were given the opportunity to join orchestra. I wanted to play an instrument so I begged to take cello. I borrowed one and broke my right arm the next day playing kickball on recess. So I didn't get to play cello after all.
When I started 7th grade I guess I'd had some testing done in 6th grade that showed my parents my hidden talents...possible skills, and it said I might do well in music.
So they let me enroll in band in 7th grade. Changed my life. I practiced every single day, hours, and ended up playing clarinet all the way through high school and got national awards for my skills. I took adult piano lessons in college, the group class kind, and even paid for private lessons later on. I stink at piano because I find I can only think is treble clef. I just can't get past that hurdle for some reason.
I have that old piano sitting in my house right now. I play some and my grand kids take piano and they practice on it. I love music, I sing, I play clarinet, I got a flute for my birthday one year so now I play the flute too (not well but I "can" make it sound okay), I play tenor sax, and I've even tried to play a guitar.
I am musical. My mother nearly killed that skill in me. I am so happy you allow your kids to explore music. I think you should go with it and see how she likes it. She might or might not love it but at least she got to try.
I would have loved to play the harp. Of all instruments that one makes me think of heavenly things each time I hear it.