I grew up on a farm around lots of wild animals and you're correct about rabbits though from my times of trying to catch them or saving baby bunnies from the cats. They're very observant, but I always figured they had much more reason to be from being alone and also limited to the ground without the ability to climb trees.
I've seen some birds that have little awareness (mourning doves and some sparrows). Sometimes they don't even realize you're almost on top of them until you're right next to them and then they freak out and fly away.
Eyes are very popular organ and seeing eyes and recognizing what they are looking at is very useful skill. I think animals get this skill as soon as they have enough physical computing power to achieve this task.
Apparently the rabbit knew my attention had turned. As would a crow. They don't need our special mental abilities -- language and lambdas -- to model the mental states of those around them.
(In other words, even the rabbits could tell last Saturday's party sucked as soon as they entered the room. Which is why none of them stayed.:)