You could try the Gaui 330X-S, it's about the only quad readily available in approximately the same size.
However, any large 600-700 size heli set at low rates would probably do, for orientation and if you wanted to get used to agility mode. The Tutor 600 with training gear isn't bad. I'm training my kid on it.
For a somewhat self stablising helicopter, the helimax coaxmial micro is one way to go - There is also the tiny 1SQ, it is the closest stock model I can think of to the AS3X in SAFE. But these would be smaller than the 350 of course.
Look and see in the swap pages, in case someone here has tinkered with a quad and come up with a self stabilising variation.
Addendum: You could get a Blade nano qx and just fly it around your living room too! It's cheap and the real plus is the lipos are cheap and it doesn't do collateral damage to curtains and blinds like an mCP X or bigger does when it ploughs into something. Real life sim (for a quad), Your kids'll love it, etc etc. If you have a spekky radio (and you do if you have the 350qx), don't think, just buy the nano qx.