Yes. It is.
What is the point of a defensive round? To punch a hole in a bad guy, make him bleed, maybe break a bone or two or rip through an organ that will bleed badly. The only point of a defensive round is to disable a bad guy through injury.
Can a .380 do that? of course it can. Is it the best, or even optimal round for self defense? Of course it isn't the very best that you can get.
Can a 380 pistol with proper ammunition cause disabling wounds, and also be easy to transport and use, and be used effectively enough to hit areas that can disable a bad guy who presents a threat, given training and skill, and successfully putting rounds into a good place to cause serious wounds?
Are you tired of hearing me say 'yes'? of course it can.
most rounds can do so. Most rounds can disable a bad guy, but when you go below this level your chances of creating a disabling wound are getting really slim.
That taurus in that round can disable a bad guy. Will it do so without fail? Gimme a break, even a round of buckshot may fail to stop a bad guy.
So, I see only a few questions. Can your daughter make effective shots in target zones with very effective 380 rounds? will that taurus reliably function and put the rounds on target? Can the best available rounds in that caliber cause serious damage, especially when three rapid strikes get into upper torso? If these answers are to the affirmative, then this weapon and caliber are adequate for the job. That's just as simple as it can get.
Now, could she move up to a 'more effective' gun, like the 9mm, 40 caliber, or 38? really, can she do it? fit a bigger gun in her purse, shoot that bigger gun well, and in light of the other obstacles of the larger gun and caliber, carry that weapon every day and night when she believes that she will need to?
there is the very most important question. Can she use a bigger gun or not? if it is going to interfere, and make carrying more difficult or shooting more difficult, well, getting a bigger and more 'appropriate' gun is a dumb decision.
A pistol of 380 or above will effectively cause a dangerous wound. Every step upward in power will come at a price in controllability, and usually, size, and difficulty with concealment.
Let her get used to the 380 and practice with it, and see if she can become proficient. Then, try her out with larger, more effective rounds, and determine if those larger and more powerful guns are as convenient to carry and easy for her to use.
IF she can handle the 380 well but the other choices are not as user friendly, there is no further debate. Let her use what works best for her, and take it on faith. There's no guarantee that shooting a 9mm or even larger round will disable a bad guy more effectively. Using a different gun that she can't shoot well, or carry properly absolutely destroys any argument for using that gun.
It is better to carry an entry level, yet still effective handgun that she is proficient with than to accept any possible downsides that come with using any other gun.
Teach her to use that thing, keep it clean and maintained, use proven ammunition, and make her learn to use it well. Otherwise, it doesn't matter what the heck she is using. A miss doesn't cause any damage. A malfunction doesn't either. And my god, if she didn't carry her 1911 because it made her purse too heavy, jeeze, I hope that her insurance is paid up.