Before venturing out on your journey, take the camper out for a few miles to flex the spare tire. After driving around a bit, you may find it has dry rot cracks. If so, that's not good. Inspect it carefully for dry rot cracks after taking it on the road for a little bit! If you have any signs of side wall cracking, it's probably best to replace it.
FYI, I had original Duro tires on my previous camper. They lasted 3 years and started dry rotting. I got by for 1 more year, but then switched all 4 out before anything happened.
All I can say is, give it a try. But definitely take the camper out for a little drive, then inspect BEFORE your trip and in plenty of time for you to get new tires if you need.