Upper body strength is the key.....some kids are ok at 11 ....some aren't until 18 or even older....
They have to be strong enough - to balance their stance properly without leaning back at the waist ( so they need upper body strength to hold and swing the gun both left and right when there are 2 crossing targets in the air ....and execute 2, smooth shots ....like on skeet station 4 as an example.)
Weight of the gun is another factor ...and balance ...and recoil management. If you have a fixed breech gun ( pump, SXS, or O/U ) you're going to get a lot more recoil than with a gas operated semi-auto...and there are 12ga's at 6 lbs ....clear up to 10 lbs....
so there isn't a generic answer..../ but I would probably look at a gas operated semi-auto like a Browning silver Hunter model as a good entry level gun.
http://www.browning.com/products/catalog/firearms/detail.asp?fid=020B&cid=011&tid=350
they make it in both a 12ga and 20ga....and 26", 28" or 30" barrel...and I'
d probably look at the 26" or maybe the 28" with a young shooter...
When can she compete...whenever you pay the fees
..../ compete is a relative term vs just having fun. The first gun I used for my kids and grandkids was often the 28ga... but you have to reduce the recoil...and keep it within limits that suit their strength and body style...
transfer the gun to her name ...check the laws in your state...