A much as I would like to recommend a sponsor here, when it comes to price/performance and adaptability, it would be the Ragim Matrix Junior 48".
Now girls usually develop a little bit faster, but with limbs available in 12,16,20 and 25# @24" this bow will be able to grow a bit. It also really depends on her size and strength. Depending on the height of her parents/grandparents, she may outgrow 48" quickly. Really depends.
With some cedar youth arrows from Wapiti Archery, this bow is a combo that can shoot in the top 3 in the IBO Trad World Cub Class. I train the IBO Trad World Champion who won two years in a row in the Cub Class. Good equipment will go a long way with keeping at it. Important with the Ragim Matrix Junior: ditch the factory string, replace with an 8-10 strand B50 string with padded loops and wrap the string ends with some wool and put small wool silencers in there for the joy of a quiet bow. The brace height should be around 5.75-6" with the new string. You will be surprised. I would recommend starting with the 16# limbs, most 10 year olds should have no issues, unless they are really tall and have a longer draw length. Black Rhino is probably also a good address wit their buy back program.
Now, the Ragim Matrix is made in Italy and not in the Far East.