Hi,
The export will handle the name and image of the categories and their structure, but not all their fields (meta description, description, alias, canonical URL, etc).
If you don't use them, then you'll be good. Otherwise, with the CSV export/import, you'll get your category structure with the names and images, but you'll have to enter the other information manually.
Alternatively, you can go in the hikashop_category table of your database, export its content and import it in your new website's phpmyadmin database after installing hikashop and you'll get you're category structure.
Of course, you still need to copy the image files from the media/com_hikashop/upload folder of the old website to the new.