I totally understand your concerns. But a good dojo will train responsibly. Football, girls soccer, and gymnastics to name a few have significant injury risks—far above martial arts.
Why would you be more concerned about girls getting injured? Self esteem, mental toughness, and physical fitness all trump a few broken bones in my opinion as a parent of girls.
My tattoo artist is a nationally ranked no-gi BJJ competitor, and her daughter is well on her way. If you asked them, I’m guessing they would emphatically disagree with your concerns.