I'd agree that there are some animals that don't seem to be aware of this, but I can't think of any birds or mammals I'd put into that group off the top of my head. What makes you think this is uniquely human?
Well, I don't see any ducks around here postulating what it means to be mortal.
But in all fairness, I think you are most likely referring to the "fight or flight" response mechanism found in living creatures. This is simply an unconscious reaction to stressful stimuli and doesn't signal a higher state of consciousness.
I'm not sure what your basis is for either claim. How would a duck that was aware it could die behave any differently than what we observe? What makes you think that fear is a conscious emotion in humans and an unconscious reaction in animals?
If you were a member of an alien species briefly observing the Earth 50,000 years ago, you'd probably use a similar argument that humans aren't conscious. Sure, they hunt, they play, and they show fear of danger, but that isn't substantially different from other mammals.
