She is 10 this year.and is good at shooting woodchucks.
She went hunting with her Father and got to see a Deer killed and gutted.
She has no problem with it.
The 7mm-08 is a good cartridge but it's more recoil than I'd expect a 10 year old boy or girl to shoot well unless there are big for their age and much less sensitive to recoil that average. Hurt them once at that age and it can turn them off.
If it was me, I'd do a lot of chuck hunting with that .223 and introduce her to a .243 shooting the 95g NBT a few rounds at a time. It's about half the recoil of a 7mm-08 and quite effective on Whitetail out to 300 yards, Mule deer to 200 yards. If she hunts with the .243 for a few years, when she's 16 she'll be ready for a 7mm-08 or heavier rifle.
That said, there are girls, like my niece (22years old - former HS and college basket ball player), who like big guns, wouldn't know how to flinch, and are scary good shots right out of the box. She has put as many as 300 rounds downrange in one session from my Glock (only stopeed because there was no more ammo), shoots my .45LC Ruger BlackHawk with deer loads in it (255g LSWC over 10g of Unique), and can shoot my 1953 .30-06 Winchester M70 (with a blued steel butt plate) just fine. But she was never pushed, never made to do anything with a rifle or handgun that wasn't fun. So she never got turned off.
She hasn't been willing to shoot her dad's 12GA slug gun yet, but she's shot my daughters 20GA with 3" buckshot loads and handled it just fine.
Fitch