Several good options out there but it would be easier to make a recommendation if we knew a little more about her. For smaller framed shooters, I like the 7mm-08, the .308, and the new 6.5 cartridges. Ammo availability has changed a bit over the last few years. Hornady's current top produced caliber is 6.5 CM. Of course, .308 is readily available as well. With that in mind, I would either go with .308 or 6.5CM. If 7mm-08 ammo was more readily available, I would steer you that direction as it hits the sweet spot for power vs recoil imo. That is what my wife shoots and has taken elk, deer, antelope, etc with no problems out to 300 yards.
Any of the 3, with quality bullets, are enough for elk, moose or bear at reasonable ranges. Since moose is on the menu, the .308 probably wins for me since it has such a wide range of factory projectiles. It's pretty easy to find 178 or 180 grain loads that would be more than suitable for elk and moose but it could be loaded down (for lighter recoil) for deer and antelope, if you choose to.
Now if your daughter is tough as nails and recoil doesn't bother her, by all means go bigger if that's what you and her want. Insurance never hurts as long as she can shoot it well.