Since it was brought up: The Baikal IZH43 HUNTING SxS comes in the following gauges, 12, 16, 20, 28, .410. The problem I see with the 28 is it has fixed chokes and expencive shells. You will find the same issue with a .410 however. IMHO a child should start on a 12ga with light loads or a 20ga. The .410 is a little recoil gun, but it is hard as heck for a beginner to hit anything with a .410, heck it's hard for anyone who isn't used to it. Just my thoughts on the matter. Oh and I would not say any of these guns would be a waste of $350. Look at it this way:
A new Gun: $299
A box of shell: $5
You get to help your daughter fuel a love for shotgun sports: priceless