Now are you talking about a subcompact or a pocket gun, because .380 handles differently in those two platforms. .380 in subcompact isn't bad to shoot, but .380 in a pocket gun is gonna be painful. My little Seecamp .32 is one of the hardest guns to hold on to that I've ever shot, and the .380 version is even worse. Find a range that rents the gun you're thinking of buying because some of these little guns are monsters to shoot.
If a .380 is comfortable for her to shoot then go for it. It's got more than enough power for a carry gun. Fmj in both .32 and .380 can do 15-16" in ballistic gelatin which is comfortably within the fbi standard that everyone cites. The fbi standard is if the bullet penetrates less than 12.5" it is inadequate, and if it penetrates more than 18", it is still satisfactory but not optimal.