Hello Mandy,
How great to hear you'll be visiting the island next year! There is indeed a
ferry from Holyhead to Dublin as you mention.
As for campsites around Belfast, you can use platforms such as
Camping Ireland to find suitable options. I've found a couple of options around the
Mourne Mountains too for example. They have a
handy map which allows you to zoom in and see what's available close to Belfast. You can also check out
Campercontact or
Pitch Up which have some options showing up in the surrounding area. This article here about
camping on the island might also be useful to you.
I hope that helps in the meantime, but if you'd like to share some more details of your itinerary, I'd be happy to help find additional suitable locations.
Warm wishes,
Alex