I stared at mine for about half an hour before I asked myself that question. LOL
I keep mine on the counter until I get more than a dozen, then I either hard boil the old ones or go ahead and refrigerate.
Do this: examine your first egg cracked in a bowl to see first hand how your fresh egg looks. Fry and eat it and compare to store bought egg. Then keep what you get from the girls (all of them) on the counter, numbered in sequence (to track age) and eat as needed using the smallest numbered egg. Note the difference (if any) in texture/flavor between birds (I tend to prefer my RIR). Most importantly, note changes in the firmness of the whites when cracked. Whites get thin with age. Yolk color varies with diet (more greens for orange yolk).
When There was noticeable aging in the whites, I go ahead and boil or fridge it. With only three, i rarely have any sitting in the fridge.
(edit: this gives you an idea how long your eggs will remain fresh. I imagine it also depends on how warm your house is)
From a cooking standpoint, room temp eggs arebetter to work with.