You're the landlord, but you're also now a roommate. And good roommates divide up the chores.
It should go without saying (it should, but we've known too many grown men whose mothers still do their laundry when they're home) that your kid washes his own tighty whities or vacuums her own room, but the common areas should be split up.
It's best to have a schedule. Every Sunday, for example, the living room has to be dusted and vacuumed and all wood surfaces polished. You could either switch off weeks or assign the task exclusively to one person. (If one of you really hates cooking but doesn't mind doing dishes, it doesn't make sense to rotate the cooking duties.)
Running a household is a lot of work. Your kid can take care of the grocery list this week and run some errands while he or she is out pounding the pavement. Consider it (and treat it as) training for the future in what it means to be an adult homeowner and member of a family.