A 6mm Remington would be a great round to start her off with. Loaded with an excellent 100 gr. Partition similar bullet and it would work fine even on an elk. The 25-06 is another one to consider, or the 257 Roberts. One of the things I did with my son when he first started was I made sure and had him shoot with soft plugs in his ears under his muffs. The noise is something that is really distracting to a young shooter and I feel it makes the "kick" seem much worse, or at least that is what they perceive. Have her get lots of practice and another way to make it so they don't concentrate on the recoil and more on the shot is to have some type of reactive target, something that provides immediate feed-back. A round steel 5" plate at 100 yards, old bowling pin, and you can even get some relatively cheap stuff you can shoot that explodes!! Make sure it's fun for them, always try and keep it a lot of fun.
Best of luck to you guys.
My son Jeff and his first elk. One shot at 350 yards with his 6mm shooting a 90 gr. Nosler E-tip. Hit her right behind the front shoulder on the right side and the bullet angled forward and exited her left shoulder. She went 20 yards and dropped.
Andy with his dad and my son Jeff with his first big game animal ever! One shot at 250 yards with my 25-06 shooting a 120 gr. Partition. She was angled and he hit her perfectly on her left side where you can see the spot back towards the rear of her ribs. It angled forward and exited just behind the right shoulder. She ran about 40 yards and went down.