It's not a question of which hand is more coordinated, as in throwing or writing. Just because she is a lefty at the things that we identify as lefty, it doesn't mean she is lefty musically. It has to do with how the roles fall within our body, not where the coordination is. I know plenty of lefties who not only don't play music lefty, it would be totally unnatural to them. They didn't have to learn the other way, they are playing the way they are predisposed to playing.
Think of it like a drummer. For example, I'm a lefty musician. The downbeat is in my left foot and also in my left hand. As it turns out, coordination-wise I'm virtually completely righty. But if I sit on a drum kit the downbeat will not naturally come out of my right foot (where the kick drum normally is). The accents come naturally to my right hand, not the backbeat, which is what naturally goes to a righty (musician's) right hand. You sometimes see drummers like Lenny White, who play on a righty kit (they don't switch it around) but they play with a lefty's roles in their hands, and they learn to make the kick happen with their right foot (usually because it's their stronger foot, as it is with me).
Generally, most lefty's are not lefty musically. It's just a different thing, a different part of the brain, than what governs coordination and strength, or the side you favor.
Here's a test I do to see if someone is a musical lefty or not: play a simple drumbeat on the table that has a simple kick/snare rhythm. I tell people to go boom/pop, boom boom/pop, boom/pop, boom boom/pop and I don't tell them how to play it. And then move it up to boom/pop, baboom boom/pop, boom/pop, baboom boom/pop. Nearly always with righty untrained musicians the boom(kick) will be with the right hand and the pop(snare) will be the left.
Try this with your daughter. I'm interested in what happens. She's more likely to be a natural righty musician than lefty. : )
Hey M0ses! You must have posted while I was thinking what to write! Yup, me too. I am completely righty in all of the standard stuff. (Interestingly, I realized that I use my left eye when using a camera eye piece.) But in stringed instruments, drums, anything musical, it's lefty.