I have done this a few times. The camper will likely be a full time rental camper so expect it to be a little worn. The three we've rented have all worked fine with only cosmetic blemishes.
We've rented from our home area, once from Midland (on the way to the Davis Mountains) and then once in Arkansas from a guy who lived near where we were camping. I would highly recommend trying to find a camper as close to where you are going as possible. While it seems a bit risky to find out exactly what your accommodations are when you get farther from home, not towing it for several hours is a treat. In both cases where we rented away from home it was great.
In Arkansas we paid an extra $75 for set up/tear down which meant we didn't deal with anything including the dump station and we saved over an hour on the front end and got to just leave at the end of the trip.
When we picked up in Midland, we met the guy at his house and had previously discussed all the dishes/equipment he provided. I hooked up to make sure I knew how his set up went, and we were off. This took maybe 30 minutes with BS-ing about midland and camping.
When we picked up in our area, we had a long drive the day of departure so I went the night before. I had to drive 30-45 minutes to get the trailer, hook it up then come home. Then had to pack everything, then depart the next morning. We had to do the reverse upon return which added a total of several hours of effort.
Pick up on the way out of town if you can. And drop it off on the way back. You'll save the gas and pain of several hours of driving nowhere near your destination.
The experience with RVShare itself was incredibly easy. Be mindful of how they try to tack on insurance/coverages as they seem to require some amount but also offer additional levels of service. In two cases the RV was returned with no problems and I got an email the day of indicating the RV was in good condition with no charges. In one case the handle you pull to open the gray/black tanks wouldn't close. I disclosed it to the owner and I also got an email with an indication of no damage. So I got my deposit back on all three quickly.
Also, look for campsites with full hookups that include waste dumping at the actual site. This will make a huge difference in convenience as you'll actually dump while the trailer is in place and you wont have to move the trailer to the dump station or fill up the portable dump tank to transport to the dump station at the campground.
Verify the electrical needs of the trailer. Don't book a 30A site with a 50A trailer.
And if you haven't towed a trailer before, do yourself a favor and look for pull-through sites were available.