T., My husband and I build pools and we advise against chlorine systems, because there are lots of studies that indicate some serious issues.
Just remember whatever goes on the skin is absorbed in the blood stream. In addition to absorbing the chlorine through your skin in a swimming pool, breathing it is also not good for those little respiratory systems. If it is your own pool, I recommend putting in either a salt water chlorinator or some other alternative sanitizing system. If it's just on vacation, then I recommend limiting the time you are in there iwth your daughter, and look for any signs of distress or labored breathing. I'm not a medical professional or scientist, but this is certainly my recommendation based on the studies I have seen.