My DD had a 32" Mizuno GXC102 catcher's mitt. It was soft, had a power close, and a broken-in feel, which made it nice for her to start out with - plus I think I only paid $40 for it.
Personally, we wanted our DD to get used to a catcher's mitt, though I saw a lot of girls that age just using the regular glove. We also didn't want to go too expensive, as she would be growing out of it - or even deciding not to play that spot anymore.