Well, on one hand she doesn't squel, giggle, jump up & down then promply swing around and point the thing at your gut when she manages to hit a piece of paper with it. So apparently she has the maturity and presents of mind to know that these things are intended to drill holes in what ever they are pointed at.
On the other hand, if she really knew what she wanted, she would tell you and be able to offer a convincing arguement to support the decision.
It's my impression that she is reasonably mature, is not frightened by guns, is willing to learn proper gun handling - but is really not familiar or comfortable enough with guns where you would even have to ask the question.
So, given these assumptions (and I know the old line about "assuming" things), it would seem a revolver would be the best choice. Very simple, very safe and perfectly adequate for the purpose intended. Blue or stainless steel would be better than light weight alloy (to dampen recoil - and in a purse weight won't be much of a factor). Short barrel (to aid in weapon retention in a close struggle). Small frame (typically fits small hands better). Nothing larger than .38 (adequate for defense - but controllable for most any healthy person).
S&W J frame or Ruger SP101. Both are top quality - and reasonably priced - so why mess with anything else? If she really wants an auto, get a larger frame .22 (like that Slabside Ruger) so she won't be inclined to carry it around - but may be inclined to take it to the range and shoot it often. I expect that if she tends to favor autos at this point, it's because the .22 she's shot is quite, low kicking and easy to hit what she's shooting at with minimal skill. Is she loading the magazine, racking the bolt, clearing the jams & cleaning the pistol all by herself - or are you "helping"? Handing a young and inexperienced person a smaller frame, larger caliber auto for concealed carry is inviting disaster in my opinion.
Some other things to consider. She's going to college, right? What do college kids do? If you don't know or don't remember - they drink, go to parties with people they don't really know, pay more attention to impressing each other than making sure their belongings are secure - and in general do silly kid stuff. Good, that's what they are suppose to do at that age. But is a gun the appropriate sort of thing to be introduced into such settings? I haven't been in college since bell bottom pants were popular - but experience with my own college age children indicates things haven't changed much. I don't carry at parties. If I stop off and have a couple of drinks with friends after work - the gun goes in the trunk of the car first. I never have an unsecured gun (even in my own home) when others are around. Will your Daughter have that kind of dicipline?