I'd recommend going with a 20ga over the .410 ro 28ga. Ammo will be easier to find and cheaper. The 20 is a pretty good shell that offers some flexibility.

Look for a gun that has a stock that can be extended or changed out as your young hunter grows.

My fiance shoots a Rem 1100 LT-20 that was cut down to fit her length of pull. It's chambered for 2 3/4" shells. So far she's taken ducks, pheasant and her first turkey with it.