I would think that the "quick" answer is...maybe.

2 ideas come to mind. First, you might be able to drill a hole thru
the gear and shaft and place a spring pin to lock them together. This
depends on the pins you can get and the size of the gear and shaft.
Second, and I know this is scandalous to say here, but, since this is
for the kids to play with, have you considered epoxy?

Both of these methods will prevent you from having to machine a new
gear.

Hope this helps,