Does this fall under the category of a design patent (on a specific rendering / likeness)? Does this instead come under the level of copyright?
It depends, the work can be protected as a design patent or under copyrights.
- Design patents are for the visual appearance of a product and are intended to be applied for industrial products. More information here. You can apply for a design patent but the disadvantage is, design patents have a limited term.
- Advantage of copyright protection is, copyright duration in US is 70 years.
So the author of the work has to choose which one suits him/her best. Another interesting information I came across, thanks to this question, is that, in the US there is a separate provision for design protection it can be found here. I am not much educated on this one, so you will have to check it out.