The spine is one of the last things to fuse on a horse. The bones fuse from the order bottom up. Jumping causes impact to the joints, tendons, and the spine and those are things you certainly don't want to go on your horse.
I think the earliest you should ever jump a horse is four. Personally I'm waiting till 5 with my boy before he even goes over a tiny cross rail. I know it sucks to wait especially if it's you're only horse at the moment (like me) but in the end I'd rather wait a few years and him last a good 15+ riding years than start earlier and cause arthritis and other health problems.