How big are the barrels? Normal sized?? How long has he/she been jumping? How much have you been doing with him/her? I like to stick to smaller fences until they are well balanced on the flat. But, if he/she is doing well then you could probably jump barrels (laying on their side I hope!). Just go slow so you don't scare him/her. Good luck!
In my opinion you shouldn't. She might be really good at it and show no signs of being unhealthy but down the road you might regret it. Most horses don't even start under the saddle training until they are 3 or 4. Don't rush anything!