Three things, from reading in between the posters arguing about something else entirely...
One, the DD had no other place to kick the bratty (and deliberately offensive) pest than in the face, since that was the bit of the brat that was invading her space in a completely unacceptable way.
Two, we don't know whether DD had her shoes on or not, and that makes a huge difference. If she did, then yes, the brat was more likely to be hurt; if she didn't, she could as easily have broken her toe as broken the brat's nose. Always supposing it was a hard kick; this doesn't seem to have been the case, since no actual damage seems to have been done.
And three, this whole incident sounds to me as if it happened in under a minute; the chances of finding a member of staff in time to do anything to prevent the nuisance are nil, I'd say, and if the adult mother had physically removed the brat who was invading her daughter's privacy she would herself have been liable to censure: you cannot just manhandle other people's children and assume it's not going to cause a ruckus.
(In passing, people keep saying "she was behind a locked door". Really? She locks changing room doors against her mother? And if she was, it clearly wasn't a sufficient protection against someone whose age DD did not know and possibly whose sex she wasn't sure about either, getting in there with her, even if it was only their head so far.)
OP, I wouldn't blame DD; I wouldn't even blame her for saying in the heat of the moment that she wished she had hurt the other child badly (which to me suggests she knew that she hadn't kicked hard enough to do so). I would at a later time have a chat with DD of the "I don't blame you for what you did, but I think it was a bit of an over-reaction and you might get into trouble for doing it; if something like this ever happens again, what else might you do that would be better?" type. The sort I had with each of my daughters in turn when they finally lashed out against someone who had been going on and on at them until they felt threatened.