In FarmVille 2, the Dog House, along with other animal cabins such as the Cat Cabin, is considered a workshop. As of now, there is no way to delete these structures from your farm. This limitation applies to both the Dog House and Cat Cabin, making them permanent fixtures once they are placed on your farm.
If you find that these structures are taking up valuable space, you may need to rearrange your farm to accommodate them more efficiently. Unfortunately, the game does not currently offer an option to remove or delete these animal cabins.
For any updates or potential changes to this feature, keep an eye on official announcements from Zynga or check in with FarmVille 2 communities and support resources.