first, remember material possessions are not worth killing anyone over.
Second, contrary to what TV and Movies would have you believe, handguns are not magic wands, not all badguys will stop from one bullet. If you really want to stop someone, use a shotgun or rifle. Unfortunately, shotguns and rifles don't fit well in a nightstand.
Shoot the most potent handgun your daughter can handle. Don't let anyone push a little .22 or .25 on you, or a light weight snubnose. Also remember, small light guns kick more than heavy ones. Yes, doesn't seem right at first but think about it. For beginning calibers i suggest 38 special in revolver, or 9mm in semiauto
Revolver
A great place to start is with a medium sized revolver with a 4 inch barrel. you can get a 357 revolver and shoot 38 specials out of it. Look for a Ruge GP100 or SP101 (even if they are snubnoses they are heavy and solid, the 3 inch barreled ones are great) from ruger, Smith and Wesson model 10, 19, 66, and 686, and Taurus.
Semiauto.
Something to consider with women and short men. Your hand needs to fit the gun. See, many 9mm semiautos are 15 shot models, the way they do this is to have two stacks of 7 side by side in the grip, with one on top. This makes the grip fat, often fat enough to cause problems. I would suggest getting a semiauto built around a 7 or 8 shot magazine (not 10, that is double wide as well, just shorter). Sometimes such thin guns are also made extralight for concealed carry, you don't want that as it will kick more. Look into the Kahr K9 stainless steel, the Smith and Wesson 1319, and it's economy brother the S&W 908, the Walther PPS (Not the PPK, it should not look like sean connory as james bond's gun) the Sig 239 and the Sig 225, all in 9mm. The sig 225 is one of the models the FBI allows people to carry in lue of their standard duty weapon, specifically with the idea of a woman or man with small hands making that selection. Some very large police department in Europe just sold a TON of slightly used 225s, you can get them four about $250-300, in very good shape.
If a medium sized 38 special and/or a medium sized 9mm recoils too much, you have two options, a revolver in 32 H&R magnum or a 380. Again I recommend the SP101 or the Smith and Wesson for the 32, and the Beretta Cheeta model 84 380, or the Sig 232 in 380, very solidly built guns with good heft. Unfortunately, these are harder to find. Especially with the 380, many many of them are desgined for back up carry, and they are small and light and have almost no sights. These light guns can actually recoil harder than a medium solid 9mm. Also, any gun that looks like a Sean Connory James Bond gun, that design (walther PPK and look-alikes) is notorius for biting the web of the hand, the one exception is the abovementioned sig 232. Stay away from Kel Tec, what they do they do great, but that is light small concealed carry, again, the opposite of what you want.
If you are totally set on getting a tiny little purse gun, then I would recommed the Beretta Tomcat in 32acp.
Take a NRA basic handgun class.
Remember the 4 rules of gun saftey
1.Treat all guns as if the are loaded, with absolute care and respect. (if anyone hands you an unloaded gun, check for yourself, or have htem show you how)
2. Keep your finger off the trigger until your sights are on target and you are ready to fire.
3. Never let the muzzle of the gun point at any person or anything you aren't willing to see destroyed. (this includes 'unloaded guns', be especially careful when picking up a gun, it is easy to forget and point it at people just as you pick it up)
4. Be sure of your target AND what is behind it before you shoot.
I would also suggest the website www.corneredcat.com