I would say the same as Alinde: it depends on when you are planning your road-trip! The Defender would be nice in the summer months (especially if you are looking for one with a rooftent), but not mandatory as you wouldn't really need to go offroad on the island (and note that overnight parking is only allowed with the permission of the landowner and/or if there's no interdiction sign)
I haven't seen any overland vehicles or Defenders at campervan rental agencies though, so I would go for a smaller campervan that can manage the narrowest roads (like a Ford transit or a VW transporter for instance), or perhaps look into renting from individuals. In addition to the ones Alinde shared, the Camping Ireland website
has more rental agencies that you may want to check out.
I leave you with these few tips on exploring Ireland by campervan
. Would it be your first road-trip on the island?