You may be familiar with the rabbit from Alice's Adventures in Wonderland as illustrated by John Tenniel.
But my rabbit does not have a pocket watch, yet she often manages to get up on the bed minutes before the alarm goes off. The only clock in the room is a digital alarm, that it is not possible to see unless you are on the bed, so I can't see her checking it through the night without waking me up. I have heard from a few others who share a bedroom with a rabbit that it is not unusual for them to be up on the bed shortly before the alarm goes off, for some snuggles.
Unlike cats and dogs, rabbits seem to prefer something solid under them when sleeping, so they generally move to the floor for the night. Maybe once a month or so she will wake up in the middle of the night and get up on the bed, grabs a quick snuggle and back to the floor, but usually she waits until 5 to 15 minutes before the alarm goes off.
If the alarm clock was a wind up, you could make the argument that there is a sound made by the clock before the alarm goes off. But the only non-digital clock in the house is a battery clock in the kitchen (she does not have physical access to the kitchen) and it does not have an alarm.
Can Rabbits tell time? Or maybe the better question is; How do Rabbits tell time?