Shit (excuse me) I thought this was a folk music newsgroup; why this sudden concern with reading from music . . .Whatever you do, encourage her to sing, to develop and stretch her voice. That's a far more fundamental instrument than the piano or anything else . . But the "go with her enthusiasms" is certainly the first rule.
I don't know what prices are like in the US, but in these parts you'd get a perfectly adequate fiddle or guitar for about 25% of the cost of an adequate electronic keyboard (and and adequate real piano is even worse); a suitable keyboard will be fairly heavy. But, as stated, avoid very cheap instruments. If buying a fiddle or guitar it's worth taking someone who plays the instrument with you to make the purchase, and going by their advice. If you're prepared to accept an instrument which is a bit battered in appearance then you'll get (musically) far better value for money (you don't want to see the fiddles in our houshold, but they sound fine). And - in case your daughter changes her mind later - fiddle and guitar hold their value much better than electronic keyboards.
Some 10 year olds find the "mechanics" of a guitar a bit limiting (may depend on the size of the 10 year old!!), but at that age I wouldn't worry at all about the "having to hear the pitch" argument on fiddle - indeed, that's exactly the skill you want her to develop.
To return to my first point - our experience is that it's MUCH harder for someone who's learn music from the "theory and score" to learn to play by ear than it is to go the other way. But ideally develop both sets of skills in parallel (and it's well worth looking round for a teacher who is sympathetic to such an approach - which seems more usual in violin/fiddle teachers than in piano teachers). And you MUST go with a teacher with whom your daughter is happy . . .
(Speaking here as a non-musician in a family of musicians, two of whom teach both "clasically" and by ear.)
G.