All of the suggestions are good ones. Including the 7.62x39. I have taken 11 deer with this caliber using a Colt Match Ar-15 using cheap soft point ammo. I have only had to track one of them.
Another consideration, if she is recoil sensative or is thinkig about a certain caliber but is unsure of the recoil, I recommend a Limbasver recoil pad. It adds a couple of inches to length of pull but its the best $30 I spent on an accessory yet. I use it on a Ruger M77 in .270. I am kinda recoil sensative now that Im getting older. Before the limbsaver, I could only shoot 4-5 rounds and I had to put it down. With the pad I can shoot a whole box and not feel the pain.