Put the foot down. Rugby is sometimes a dangerous sport, everyone gets injured at intervals its a rough sport, but the positives far outweigh the negatives. As long as you're not reckless and do what your coaches tell you, chances are you won't get seriously injured. Its a great sport with a great ethic. You need only look at how down to earth most pro rugby players are. My Dad always loves telling me about how rugby is a game anyone can play at some level.
Hello - maybe take her to a match, tell her it's going to be an Olympic sport (at least Rugby 7's is going to be) ... maybe get her to talk to a coach for some reassurance about the training and injury prevention ... I have two daughters and two step sons who all played ... one of my daughters still does.
Most coaches are more than willing to spend time to talk to/reassure parents, if it means more people playing the game ... hope this helps, and welcome to the forum