My grandson is 12, 5'1" and 115 lbs. Shot his first 2 deer with his Dad's 270. I can't recommend this approach as we are having a difficult time getting him to practice with the 270 due to the "Kick". (Son-In-Laws, can't live with them and can't Shoot Em')
IMHO - It still comes down to bullet placement and a competent load that can do the Job. Plenty of deer have been killed with a .243 and 6mm however, I still consider them an "Expert's" cartridge as bullet placement is even more important.
If you want an undersized individual to develop shooting skills then you should choose a cartridge/rifle combo that won't punish them each time they shoot. I prefer the 7mm-08 as a moderate recoil cartridge and I can attest that it will and can do the job on Deer sized Game.
Personally, I'm a 30-06 Fanatic and will always be (My son-in-law says that is because the cartridge came out the same year I Was Born!) That's an embellishment - and he's real good at that part.
(I'd whip him if I Could!)
Safe Hunting to All