As a copywriter, you are not going to be responsible for putting your copy into design. Graphic design is a whole career in its own right, so we do not recommend trying to tackle both disciplines at once.
At the same time, it’s not up to you to find a designer for your client. Some projects won’t need one, some clients might already have one, and sometimes your client might ask you for a recommendation. Regardless, it’s never necessary to bring a designer to the table.