Do you have a teacher for her? Even if they don’t rent commercially, many teachers keep harps to rent for their own students. If you don’t have a teacher, get one first. That is THE most important thing for a child that age.
I love the harpsicle, but I wouldn’t recommend it for your situation. It can work, And I wouldn’t rule them out completely, but if you went that route I would really push for the grand harpsicle for the range and size (and full set of levers) and at that price you may as well invest a bit more and go for the Ogden.
The pilgrim harp Tayce mentions is actually comparable in size, and string tension and spacing to the ogden. Depending on where you live that is a good choice too. Pilgrim is based in England and their harps are harder to come by in the US and Canada, where the Ogden is Lyon & Healy based in Chicago, and fairly easy to come by in the US.
But the harpsicle was designed as a light, inexpensive travel harp. While it isn’t inherently limited to that use, and can even be used professionally on some instances, I think a serious study of the harp would necessitate replacing it with something larger, and with full levers (and depending of the ultimate goal and type of music she wants to play, stiffer string tension) sooner then later.
Definitely what the others said, however. A teacher will be able to help you find the right harp for her.