Having done the nullabor a few times and over Christmas my only concern would be the heat. It's totally doable but some of the temps are insane! So even with a cooler I'm not sure how you'll go. Not meaning to scare you hon but it also depends on how you all cope with the heat over 40 and I can't cope so 45 was just crazy. My eyes were burning from the hot dry wind. And we drove non stop so we were in an air conditioned car the whole time. BUT I've noticed it's getting hotter there after Jan so you might be fine. Can you check some weather history to see what it's like?