Yes, all Happy 4×4 category campers (Happy 4×4, Happy 4×4-3pax and Happy 4×4 XL) are 4WD and Automatic and are suitable for driving in the highlands. The Happy 4×4 are equipped for the harshest Icelandic conditions and F-roads. They are equipped with a raised air intake (snorkel) so it can even handle river crossings, for example.
Even though we highly advise against river crossings and suggest avoiding it if you can, river crossings are allowed in the Happy 4×4. Read more about the reasons we advice against it in our 4×4 Campervans in Iceland post. Also, keep in mind that the following roads are off-limits, even in 4×4 cars: 337, 622, F26, F210, F578, F910, F980, F249. These roads can barely be considered roads and banning these roads is industry standard in Iceland. We will cover this in more detail during your check-in orientation.