I'm in the same position trying to figure out the best elk cartridge/load/bullet combo for my son.
Overall, that's great to hear you are going to take your daughter out hunting. Out of my own lack of knowledge, what kind of velocities are you talking about? I would personally lean towards the Barnes .308 150 grain TTSX and keep the muzzle velocities starting out around 2700-2800 fps... essentially duplicating the performance of a 308 win. I think at reasonable distances, the TTSX bullets are tough to beat because of the high penetration they provide in low-for-caliber weight bullets.
Have you considered looking into buying one of the Savage youth rifles chambered in 308? The stock will fit your daughter better, and the rifles really are very affordable. Another great option would be a 7mm-08 shooting a Barnes 145 grain LRX.
I'll load up some reduced velocity loads for practice at the range, and then also develop full power loads to hunt with. The range is where they'll develop a flinch, I'm not worried about a bit more recoil in a hunting situation.
Good luck!