I've taken a few elk with one, and a girl that we used to take hunting, took about half a dozen with a 6mm. Killed em well enough. Wouldn't be my first choice for elk though. I think its a fantastic deer rifle though.
I think I would look at a 7-08 or 260 Rem. Recoil is marginally more, and I think its offers a bit more punch, albeit minimal. I think these two calibers are much more versatile. At least you can get bigger bullets. A 120-140gr TSX or Partition/Accubond would be my minimum choice for elk. Being small you'll probably need to work on the stock for her, or find a youth model. A properly fitting stock helps a lot with recoil management. You can add some weight to the stock to suck up a bit of the recoil, as well as a quality recoil pad. When she gets a bit bigger/older you can swap the stocks and she'll have a rifle she can hunt elk with the rest of her life.
Congrats on having a new hunter in the family. Must be exciting!