Darlindeliasmom said it well, I think... depends on the child, as to what age to start. The mom/partner to the Karate instructor adds a dimension to that element too... also depends on the dojo's style and the discipline it teaches.
I would add some other considerations too: What discipline (martial art) is practiced by the studio near you? What is appealing to your dd about what she sees at the local studio? Every discipline has a style and approach to its practices and, despite conventional western wisdom, they are not all identical. What will that discipline ultimately teach her? I won't place judgment on any discipline as "better" or "less worthy" than another, each has its own merit and more... I just take martial arts training very seriously and wouldn't advocate casual use or just starting any old discipline on a lark. Each one has a result and a purpose in its Way, and that in turn has an impact on the practitioner, especially if training begins at such a young age, KWIM?
As to my own experience, I can only speak in the context of Aikido, since that's the only martial art our family has practiced (does practice... for a set of very intentional reasons).
Dd began when she was six. Ds, though more energetic and physical than dd generally, is waiting until he's six—he has trouble following directions for more than 30 minutes at a time still. We belong to a traditional dojo, very Japanese, very" proper" and formal in the training praxis. One needs to be able to listen for instructions and "do" with some ability to implement the technique, and do so for an hour. Dd does really really well with this and the impact on her as a bipolar kid is amazing. She is a very serious student and loves her instructors and Sensei.
Best wishes and intentions for you and your dd... martial arts training is
highly valuable, more so if its approached with sober intentions, IMO. Hopefully, my questions are of help to you?
