MacDuff, do you really think that your little daughter needs another challenge? Because if you do some reading, you will find that middle-class American girls in general are pressured too much.
Be intelligent!
Be talented!
Be athletic!
Be slim!

She already has school, Irish dancing and piano. The Irish dance thing, with its long trips to competitions, is no easy road. Is she also doing a sport (soccer?)

How much does she play? Does she hang out with friends, doing nothing? When does she get down on the floor and play with a baby? If she goes through a growth spurt, she needs extra sleep. Does she get it?

As for fiddle-violin lessons, if you do it, make sure she has a teacher who knows how to do it right. Her body is young and her tendons, etc are tender. Avoid a self-trained person who unwittingly damages her vulnerable system.