An update.
We decided to let DD choose as we didn't have compelling reasons to stop her if she wants to participate.
I had a talk with DD throughout yesterday about competitions. At first, DD thought it sounded like a race and the best one wins prizes. I told her that it's more like a recital and the meaningful part is getting objective feedback from professional violinists. And the icing on the cake is that as she advances, she might earn opportunities to solo with a real orchestra. To that she responded, "You mean my DREAM can come TRUE?"
I'm taking this with a grain of salt since her dream changes every 6 months or so. First, she wanted to be a ballerina (age 2.5), then an orthopedic surgeon (age 3 to 3.5), and then a jazz musician (3.5 and onward). She had never expressed any desires to become a classical concert soloist before but she is 4 and she is more than entitled to dream about whatever her little heart desires.
Anyhow, now that she has put it that way, who are we to stand on her way of reaching her dream (cough, cough)?
The probability that she becomes a classical musician is not high, but it is not zero, either. In addition, the pursuit of low-probability dreams can have benefits even if the goal is not achieved. I never became world chess champion, but the dream of becoming one motivated me to train and become a very good player.
