Ah, my area of expertise. :) I've been a professional music teacher since the mid-90s, with a BMus and and MMus degrees, blah blah blah. :)
If you're just talking about teaching something at home, with no musical knowledge yourself, I would recommend the recorder for sure. There's even programs out there specifically for homeschooling parents who don't know anything about music. :)
If you're looking into taking outside lessons, then it's pretty much whatever the child is most interested in -- with a few exceptions. A 6yo is not ready for instruments which require larger lung capacities or "wind power" -- most band instruments, in other words. Flute, trumpet, etc. Also, they require a complex adjustment - in fingering, in embouchure, and in breath support - for every single note, whereas piano and strings are more straightforward -- plunk fingers, pull a bow, note comes out. Generally, age 9-10 is considered a minimum starting age for band instruments, they have more mature bodies and can handle the coordination and control of sound production.
So a 6yo is probably ready for piano and for string instruments. That being said, not every 6yo is ready for "traditional" private lessons. I've had some students younger than 6 who definitely were, and students age 8 who still weren't. So a lot depends on the TEACHER and the class/lesson methodology, more than it depend on the particular instrument. :)
Suzuki classes, Kindermusic, MYC, these are all great options. And if she's REALLY keen on, say, the piano, then ask around -- find the local music teachers' association -- and try to get recommendations on what teachers are really good with young kids.
Oh, guitar -- can depend on the teacher as well. I've known guitar teachers who won't take kids under age 10 or so, for various reasons, and others who would.
And I would seriously recommend -- if you don't know music yourself, do NOT try to teach your child anything beyond things like the recorder. I know this is contrary to what we usually believe as homeschoolers! But I see music as more like a trained skill, than a knowledge subject. Anyone can learn ancient history on their own from reading the right books, watching a few movies, etc. But you won't learn how to figure skate very well by yourself. You need a coach. You can learn some basics, like what the notes on the page mean, to a certain extent anyway, on your own. But to play an instrument, you need a *coach*. I've seen first-hand the problems that happen from bad habits formed early -- either from self-studying kids or unqualified teachers! It is SO much harder to fix later on after the habit or misunderstanding is entrenched. They just miss out on so much. It seems easy to say "oh we'll just start with the easy stuff ourselves, then get a teacher when we start to struggle" -- but it rarely ever works that way, even with the best of intentions. Either the eventual teacher has to fix things and start from scratch ... or else the kid becomes frustrated and/or bored and quits.
(And of course there are exceptions, my own son has been a mostly self-studied musician so far, I try to help him out with some things but he does most of it on his own... however, he has an exceptional innate talent, above what most kids have -- this isn't 'stage mama' talk either, everyone is astonished by him, myself included!! -- therefore most kids do need music teachers to guide them through stuff they can't figure out themselves)