Don't know what state you are in but you usually need a license to partake in hunting (usually defined as the act of taking, pursuing, capturing, harassing, and/or killing, or the intent to take, pursue, capture, harass, and/or kill. Note this covers pursuit to just take pictures too). There are usually hunting seasons defined for each animal that minimize the effect of pressure during the breeding season (nesting and brooding in the spring for birds). Since most states recognize turkeys as a viable game species, a very popular one in most states, the wildlife law enforcement in your area would most likely frown on this idea.
So, to sum up, depending on your state, it's most likely illegal for your sister to try to catch wild baby turkeys. Also take into consideration how big a hen turkey is, and realize that a hen is not just going to let a 9 year old chase and catch one of her babies without trying to defend it. Plus, wild-caught babies are going to have already imprinted on their mother and will most likely not take food, and will die in captivity as a result of separating them from their mother who was in the process of teaching them how to forage for food on their own. Also, transporting live wild animals requires special permitting, and doing so with an intent on transplanting them to an area where they are not found currently is only allowed by permit or only done by your state's wildlife management department.
I know this because I've worked in wildlife management for 10 years and have specialized in upland birds.
I would recommend getting some domestic poults, and a lesson in disappointment for your sister, as it is easier to teach this fact of life when she's younger and still spankable.
