Very good advice!!!
I hope to get out today and do some more hands on with the Browning 1911-22 & see if i can dig up a ruger 22/45 light for her to play with.
Please stay away from the browning 1911-22...it's a novelty gun. Yes it's kinda neat, and yes, it weighs nothing. But the sights are rudimentary at best and the trigger is sure nothing to write home about. And once she shoots a bit,she will realize it's not a really good gun for anything other then casual plinking or introducing really new young shooters to handguns. I don't have big hands, but this pistol gets lost in them.
Now the 22/45 lite, she will shoot all her life, and it will still keep her interested. I find they don't have enough weight, but i'm probably bigger then her, and the one's i've shot all shot very well indeed.
Ditto on what BC rider said about the Bearcat, or the SP101 in 22 for that matter, though in the second case, you will want to do a trigger job. I want to like them, but every single one i've handled new had an atrocious double action, and a rough heavy single action....hard to believe after Ruger has the GP 100 so good these days!
For your money, the entry Buckmark at 350 is a stellar choice, but if it's too heavy it's not going to help ya.
Good luck.
Last minute thought, one of the retailers is bringing in rebarreled berreta's (71, 74? some one chime in) They are an excellent choice for small hands...and have real sights and a good trigger