not sure about the carpet, but your kid should be okay. If they got mixed kalk water on them, or even the dry powder, just thouroughly wash them off. The only real emergency concern IMO is if they inhale the dry powder, in which case you should head to an ER asap.
The Kalk SHOULDN'T hurt the carpet, but it'll leave that white chalky appearence until it's washed out. Kalk is a base, so maybe by mixing up a mild acidic solution of water and vinegar would help remove it if it's being difficult for ya.
Good luck on both accounts. If your child develops any wierd symptoms, ie a rash, needless to say get it checked immediately....although I doubt you have anything to worry about.
