My four year old (and her brother) have a piano, two guitars, a drum kit, a violin (that is too large) and a bunch of rhythm instruments. So no, I don't think 6 is too young. Just make sure you get one that fits her properly and sounds nice.
I got some great insight from a musician teacher friend of mine (regarding an instrument for my 5 year old). She said that it is incredibly difficult to get a beautiful sound out of a violin, but it is incredibly easy to get a beatuful sound out of a piano.
I'd only do a violin or guitar if you can also do lessons to go along with it. Both need to be tuned to get a good sound, and that's hard to do on your own. 6 is a good age to start lessons.
You could also get a little keyboard (a real musical one, not a kid's toy one) that she could start to use. Our dd is 5, and loves music. She's got a guitar (hence my advice about guitars) and we have a piano. She started piano this year and loves it.
I agree that 6 y.o. isn't too young for guitar or violin, if the child is interested in learning. I'd really encourage lessons though. There are some children who are motivated and talented enough to learn on their own, but most need some guidance and instruction.
I agree that you ought to get her lessons, rather than an instrument, although of course you'd have to buy or rent an instrument, too. IMO it's better to rent one for that age because it's rather expensive to buy something she's just going to grow out of. A guitar or violin in her size that actually makes a decent sound would not be cheap.
If you're looking for just a one-time purchase, I'd pick something that wasn't so hard to tune and play, like a xylophone. Even a piano will need to be tuned regularly (every 3-6 months) and one thing you don't want to do is have your child playing on an out of tune instrument as it can affect her pitch later.
I have played the violin for many years, and I'm going to be getting my old one back from my parents this year. I'm thinking I could teach her the basics to a violin and then get her into lessons if she likes it and wants to learn more. Maybe I will just rent one so she can try it out first.
We have an accoustic guitar, drums, knocking sticks, triangles, tamberines, etc in a larger box. We also have a "rock star" guitar. A gift with buttons to make crazy sounds. All these get use and I have seen as young as 18 mos play with the box, up to 8 yrs old. We had a keyboard that died a very slow death. We are getting a piano from my ILs' living room soon so that will replace the keyboard.
You could get her a recorder, drums, maraccas, a glockenspiel, a harp, a keyboard. Those things are all things my daughter (6) plays happily. She also plays with her guitar, but it's much more difficult for her to get a song out of it, and so she goes in fits and starts with it. She's not currently interested in lessons beyond informal "if you do this, this will happen" and I expect we won't get further into strings until she wants lessons.
We got DS (almost 5) a wonderful piano off of freecycle, and he is working through a piano phonics book that he loves. He has asked for a guitar for Christmas. He also wants a microphone, so I am thinking some sort of family karaoke thing!