Is {Stuffy Doll} effected by {Wrath of God}?
I ask because of indestructible.
No. {Stuffy Doll} cannot be destroyed:
702.12b (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=702.12b): A permanent with indestructible can't be destroyed. Such permanents aren't destroyed by lethal damage, and they ignore the state-based action that checks for lethal damage (see rule 704.5g).
RESOLVED
Can wrath of god be countered with counter target spell?
Yes, {Counterspell} or a similar effect would counter it. A spell can be countered unless it specifically says otherwise, like {supreme verdict}, or has split second, like {Extirpate}.
RESOLVED