The panels need to be defined within the JSON that you submit in your POST request.
The example in the docs doesn’t spell this out, beyond
dashboard – The complete dashboard model
To get hands-on with this, you can (1) create a new dashboard with some panels manually, (2) export that dashboard’s definition as JSON, (3) put the exported dashboard definition inside the “dashboard” field of a new JSON object, (4) POST the resulting JSON object to the API endpoint. This will create a copy of your original dashboard. From there on, you can edit the JSON model you’re posting in order to modify or add any panels you desire.
So to your original question, if you want to add a panel to an existing dashboard you can obtain its definition via the API, add the panel to the JSON object, and push the updated model. (keep the same id/uid and set "overwrite": true)