Another work-around I've found for this bug is to press 'E' right after throwing, if you have multiple stones.  That unequips it and has always let me pick up the rabbit with no issue.  Just make sure to press it before you start running, if you need to run.  Your weapon won't uneuip while running from what I can tell (not sure about crouching though). 

I always carry a few stones while traveling and bonk 'em if they get near.  Then I run up and wring their fluffy little necks!  Their cries are the worst part for me :(