You are probably better at knowing your abilities than a bunch of us random people on the internet.
+1
Also I don't see all the relevant information. Touring? Camping? Change of clothes and a toothbrush?
Obviously you know your ability better than any of us. I can only say how I would handle it. I don't think I've done a full century yet, but I've come close a few times, and it's always been in a loaded touring situation. Riding 100 miles, with all my gear, and getting up to do it again the next day can be exhausting for me. The two times I've come close, I ended up not making my mileage goals on the day after. But it sounds like you have a two day break between rides? If that's the case, speaking for me, if I can ride 100 miles cold, as long as I don't damage myself on the ride, I'll be just as ready to do it again 3 days later as I was the first time. Having come close to a hundred-mile-day carrying gear for a week's, self-supported touring, I feel pretty confident that I could do a trip where all I needed was a couple changes of clothing and toiletries. Doesn't mean it'd be my favourite day of riding. I usually like to plan for shorter days, but it seems very doable. It also seems like, given the nature of this trip, you might get better tips on the distance/endurance section of the forums.