The answer is "it depends."
In your example sentence, only "household" is correct. "Baking soda can be used as a household cleaner." That is, the cleaner is a thing which cleans a household. (The second sentence is awkward, or refers to cleaning a servant = "a domestic.")
However, you could say both "I need to do some household chores" (as in, chores around my household) or "I need to do some domestic chores" (as in, chores in the domestic sphere).
When in doubt: household is more likely to be correct. Or, just ask on italki! :)