It may be hard to test the eye dominance at that age. My son started shooting archery four years ago, and it wans't until this past year that I was sure what eye is dominant for him. Sure enough, he is left eye dominant and right handed. We started shooting left handed about three months ago, and he has gotten real good (almost as good as right handed). He was 10 when I was sure which eye was dominant. So what I am saying is, don't be all that concerned if you mess up on the eye dominance/shootingsituation. It can be corrected. It's not at all like an adult trying to switch. The most important thing is interest. You may want to get something like a Li'l Sentry Recurve that can be shot right or left handed:
http://www.escaladesports.com/bear-archery/detail.html?SKU=A22&subcat=Institutional%20Bow s
Oh, and get a good supply of balloons from the Dollar Store to shoot at!