I'm pretty sure it says that objects can't be doomed. I'll look into it.
Edit: FAQ wrote
In general, Dooms are persistent negative effects applied to a specific enemy that last until you choose to discard the applied doom card, you play a different doom, or the enemy dies.
Any enemy that has a doom applied to them is considered "doomed."
Note that while bosses are immune to many negative conditions, they are not immune to dooms. Obstacles with hit points, however, cannot be doomed.