You can select the artboards you want in the Layers panel, then choose either Selection with Background or Selection without Background in the Export dialog rather than choosing Complete Document. That will give you a PDF file with just those artboards in it.
First I will say that I am very happy to see this software and impressed with what I have seen so far...with one exception. The lack of a complete user manual. I don't understand the idea among developers that their job begins and ends with the software and users will fumble and stumble and guess their way to a working knowledge of the program. Video tutorials are great and helpful. So is knowing I have a reference, provided by the developer, that explains what every tool, panel, and menu option is and what it does, as though the person reading it has never worked with this software before. This is especially true for a new software that hasn't been around long enough for authors to fill the void with How To books. From what I can see the information available under Affinity Photo Help is bare bones at best and some of the bones are missing. I spent a lot of time learning Illustrator and enough of Photoshop to do what I need and I am disgusted with Adobe's switch to subscription based software availability. So the discovery of Affinity Design and Photo is very exciting to me. Stumbling through video's and searching YouTube and Google for additional information to understand how to use your products...that is not so exciting.