Actually, bloody stools are not so uncommon in younger ones, under 1 year. Our daughter had some blood in her stool at around 4 months old. To make a long story short, the reason for that was her immature digestive system...and the lesson learned for me, was don't let anyone freak you out- My pediatrician had us doing tests of all kinds, trying to diagnose her as lactose intolerant, made me go off all dairy (I was nursing) for 6 weeks, it was really frightening. Whatever you do, DON'T LOOK ON THE INTERNET FOR ANSWERS!!!! This will only send your stress level through the roof. My father in law is a heart surgeon and has been one for going on 45 years. He talked to the Chief of Pediatrics at his hospital for a second opinion while this was happening to me-and the bottom line was- if your the white's of your childs eyes are white, they are smiling, happy, eating and doing their business...they are more than likely to be just fine. The real technical things you want to look for are- is the blood red- if so, that can be as someone above mentioned constipation, basically a tear. Now if it's black, that usually means it's older and has traveled from the intestine through the stool. I would absolutely take her to the doctor, but please don't let them run a million tests without first getting a very educated DIAGNOSIS, not symptom treatment, while they freak you out and later tell you she shouldn't drink whole milk and should switch to nonfat, or something minor like that. The Chief of Pediatrics told us that the worst thing my pediatrician could have done was to stress out mommy.
Good luck with this, I hope this helps a little, though my situation was completely different being that she was so young, (she's now almost 3 too) but I wish your family the best and for a simple solution!