I spent a lot of my childhood doing axe work...would have definitely been younger than twelve when I started.
I grew up in a home (in Canada, yes) with just a wood stove for heat and lighting the morning fire was one of my chores starting when I was really young. I spent tons of time bucking wood with a boe saw and splitting it with either an axe or a sledge and wedges. I'll tell you this: when you are ten years old and someone tells you to split up a two foot thick seasoned oak round, you are in for a long hard morning!
Anyway 12 is definitely not too young to learn to use an axe. BUT! I hope that you will teach the kid what to do instead of just ordering him to get the job done...kind of a miracle I wasn't hurt as a kid, had NO idea what I was doing when I started out!
But no, I definitely wouldn't give a young kid a good axe...instead, I would give him a simple, hickory handled two-footer from Home Depot or what have you and sharpen it up for him.
Also PLEASE if he takes a good nick out of the bladeby accident DON'T whack him around with the handle, he will be bruised up for two weeks and it will cost him a win at the district elementary school 4x100m relays competition! Not that I've been there or anything!
I have lots and lots of advice on how kids should not be trained on axes actually so fire away with any questions...here are a sample to get you going:
Q: If the axe is dull, should I sharpen it myself, teach my kid to sharpen it, or just whack him with the handle and tell him his axe is too dull?
A: I would go with one of the first two.
Q: If he does a lousy job stacking the wood, should I give him a hand, or give him the handle?
A: First option is better.
It makes me laugh now but man I think the main use of that axe was hitting me with the handle, the next use was to split "spanking boards" and on some rare occasions it may have been used to help heat the house!
Anyway even if you do it all wrong it turns out the kid eventually learns to laugh about it and doesn't care and likes going and camping with you...but it takes a few years!