Does my dependent need to get their own ObamaCare plan if I am on Medicare?
If you are on Medicare your child can get a child-only health plan (either through private insurance or through CHIP) if they are under 18. Or, if they are over 18, they can get Medicaid or marketplace coverage.
The exact coverage they should get depends on if they are tax dependents or not, their income, and on what other people in your family need to be covered.
In general, it is illegal to sell someone with Medicare a non-Medicare health plan. Thus you can't have a family plan that covers your dependents if you are on Medicare and are the head of household, so other members of your family will need their own coverage.
Since the situation can be somewhat complex, a good place to start with questions is HealthCare.gov. They will be able to help point you in the right direction.