You shouldn't have a problem towing the Jayco on the island, some of the inland tracks get a bit tight in places but they are geneally fairly easy going. Best to set the camper up as a base and tour from there, no point trying to drag it all over the island and spend time each day setting camp.
I've towed ours easily across the island and managed fine with mid 20 psi in the tyres, really depends how dry it is over there.
The hardest part with the inland tracks and towing is if you have to move over usually the trailer won't follow you if there is a hump of sand in the middle of the track, the trailer will normally want to step out sideways on you so be warey of this or you'll side swipe the person coming the other way.
And reversing sometimes won't get you anywhere either, except all crossed up.
The island can be very dry and the tracks chewed up, if it rains overnight they are totally different to drive the next day,another thing to be cautious of on inland tracks is tree roots and broken boards on the tracks, you can easily pinch a tyre if you hit 1 too quick.