I am presuming she needs the handgun for Personal Protection?
Now we need to know a couple things.
Is the Gun for Home Protection?
Is the Gun for Car Carry?
Is she getting a Concealed Weapon Permit to pack it with her?
For Home and Car Carry I would go with a S&W K Frame 38 or 357 Revolver with a 4" barrel. The K Frame is Very Shootable for most anyone, and about as safe as anything you can use.
Now if she is going to Conceal Carry it, HOW & WHERE?
Is she going to dump it in her Purse?
Get a Concealed Carry Purse?
Carry in a Belt Holster?
Use a Clip on the Gun for inside the waist band?
Fanny Pack Carry?
Not Thought That Far Yet?
This is where the choices are hard. Anything with enough punch, and light enough to conceal carry Kicks Hard for a Lady. Also the Triggers are normally way to hard to pull. The only way you will ever get her to carry anything that is over about 18 oz. is for her to have had a very close call being dragged into the bushes. I have a lady friend of the family who was an ER Nurse in a large city for several years before moving to civilization. She carrys a Kimber 1911 Compact 45acp in her purse. She does not intend for them to be walking out of the Hospital the next morning after she has a run in with them. She has seen lots of shot up GangBangers, and she carrys a 45 acp. She is Motivated, your daughter probably is not.
With that said and seeing lots of handguns shot at the range. A compact version of a GOOD to GREAT Pistol is probably the best choice. A S&W M&P 9mm Compact is probably close to the top of my list. The new S&W Shield 9mm may very well be even better for a Lady to carry. I am all over Shootablilty. If she cannot hit with it, she has no business carrying it.
Being a Revolver Guy I would also have her wrap her fingers around a Ruger LCR-38 and try the trigger. She could also start off with an LCR-22 for her first gun, and as a practice gun, and pick her up a 38 as soon as you can afford it. I took the wife out the other day and she ran a brick of Federal through my LCR-22. She was doing pretty well way before the end of the box of ammo. The good point of the LCR-22 is affordability. You can shoot it all you want without going broke. Starting with a 22 is the best way to get her up to speed hitting with a small handgun. You can always move her on up to a 38 after she gets accurate with a 22 that recoils much less.
Lots of information to soak up on all the posts. Good Luck.