As others have said don't force the issue. Give her time to think about it. Remember, if she has a gun but doesn't want/know how to use it the gun could very well be a liability, not an asset. This would be my biggest concern.
Have you talked to her about non-firearm defense? Making sure the doors/windows are locked, having a charged cell phone nearby at all times (AKA her carry piece), awareness (including not opening door to strangers), etc. These may not be what you want but a good, locked door and a call to the police can be just, if not more, effective. Besides, if you ever have to use a weapon in self defense it would be very helpful to have her simultaneously calling the police (remind her to let the police know you are armed).
On the other hand, if one day she does decide she'd like a weapon, and that weapon is a firearm, then I'd suggest a .38spc revolver. No safety to forget to take off, no jam drill to learn, no stiff spring to pull back, etc. Don't forget a flashlight though!