I think this all depends on your DD. I would still not consider lessons with DD4, though she has an early and advanced love of music, for a variety of reasons. I'm sure she has the attention span and the understanding. She certainly has the drive. What she doesn't have are superior fine motor skills and self control when she gets frustrated (which happens easily). She would not be willing to be bossed around by a teacher. She couldn't be trusted not to take her frustration out on her instrument and those suckers are expensive. She would have unrealistic expectations and would expect to be able to perform at a high level sooner than would be possible. Oh, and also, her preferred instrument (for years now) is the trumpet, which obviously won't work for such a small child.
She got a fairly decent keyboard for Christmas, and has played on it a lot. And she has many other child-friendly instruments. I think that has mostly satisfied her desire to play music for the time being. We will reconsider when her fine motor skills and her self-control catch up to her interest.
If you don't anticipate those issues with your DD and she has a genuine interest, I don't see a problem with starting lessons at 3. I know a kid who started at 4, and her parents are definitely not of the pushy variety. If it's what you think is right, and you can find a teacher who agrees, don't worry about what other people think. Don't tell them if you don't want to.
Oh, and also, I did Suzuki when I was a kid, and one of the best parts was the group lessons/recitals. I would prefer a music school for that reason.
