I've seen a just-turned-7 year old, who had been doing Back Handsprings for a whole year already on old level 4, severely break her arm while being spotted by her coach, because she was just slightly off-center or something. My dd said the crack was louder than all the activity in the gym and everyone heard it. Surgery followed. So, no need to rush Back Handsprings. The goal should be good form and safety. I wish I could beg all the parents to please slow down and be amazed at each step of the journey, because it really goes by so fast, and you never know if it might be the last practice or the last meet. Injuries, growth, puberty, mental blocks, fear, etc., could all spell the end of their time in gymnastics. Believe me, I wish I could go back in time and soak up those Level 4 meets and just be in the moment without worrying about what's next.
Your DD will get her Back Handspring in due time, and might be the best one doing them because she did wait and learned them correctly and was more mentally ready for them, who knows? But unless she's going to level 3, she doesn't even need them yet. Our gym competes Lvl 1 and 2, so if it were my dd, she would still have 2 years to learn them. (Because I'm the crazy grammar police, I must point out its a Back Handspring, or Front Handspring; not a Backhand Spring. )