to check the back measurement it is really easy. Just measure her around where her bra strap would go. If she is 28 inches, then she wears a 28 inch bra. If 29 inches, then you can go up or down to 28 or 30 inch whichever is most comfortable.
The cup sizes increase with back sizes, so a C cup in a size 30 is much smaller thn a C cup in a size 34.
Unless she is very unusual, a 30 DD does not seem like the right size for a 9 year old.
my dd is now 12, and has been wearign something since she was about 9. She started with sporty crop tops, which gave a surprising amount of support and didn't look too bra like, which she wanted.
We have really struggled to find nice girl's bras that she will wear. The shops say no underwires for young girls, but when I reaserched it, that was basically because if it is a bad fit the wires will dig in, which is not good for you. dd actually find the soft underwires better, as she doesn't like the feel of a tight strap.
One big problem we have is that she will only consider plain white or beige. No frills, no colour, no bows etc. And to be fair, anything other than plain shows under school tops.