My wife and I went to Iceland in 2015, and we rented a Jimny while there. It took us a few days to get up the courage to try gravel roads, but once we did it coped fine with them. It was good for small river crossings, but on the way to the Thórsmörk we bottled out at the eleventh and (thus far) deepest.
For that particular journey we'd fallen in with a pair of Americans in a much more serious 4x4, which can be seen in this photo. They took their river crossings seriously: stopping beforehand, wading to test if it could be done, and throwing test rocks to find a shallow path if it was too deep for that. They didn't bottle out, and I believe got to the Thórsmörk, so whatever they're driving (Dacia Duster?) is up to that kind of job.
We didn't get to the deep interior, so I can't comment about what's needed there. If you do decide to go off-tarmac, make sure your insurance cover is up to it: gravel is hard on the paintwork. Indiscriminate off-roading is illegal in Iceland (I believe), so only use official gravel roads. And (iirc) nearly all Icelandic cover is voided for damage done whilst actually crossing rivers, so caution is needed at all such crossings.