I can't think that this would happen at this age, but what about diabetes? I know it happens early sometimes.
Too much water, and she will lose a lot of water-soluble vitamins, and that could be harmful. You CAN overdose on water.
Another thought, long shot but best said than found later: The part of the brain that triggers that feeling of thirst - maybe it is being triggered by something. I hate to be alarmist about something that might be simple. I'd rather be extensive and find out it's nothing, than to sit back and possibly lose my child.
If the pediatrician is not worried, and you are, get a second opinion. If s/he can't find what's going on (even if it is simply that she's thirsty), find someone who will tackle the question of why your daughter is 'compensating' by getting water by alternate means. (Not fond of the word stealing and child in the same sentence!)
Children compensate for lack as a matter of course.