I did something very similar last year. I rented a travel trailer for a long weekend where we arrived on a Thursday and departed on the following Monday. We have a very good idea of what floorplan and brand we wanted to go with (which is the one we now own) so I found a rental unit that was the same brand. This allowed me to do several things, experience towing such a large trailer, ensure the wife and kid enjoyed camping, see how the brand held up to heavy use (it was some where around 1 to 2 years old when we got it) which may equate to a full 10 years of our own usage. We all really enjoyed it and ended up buying a trailer a couple of weeks later.
You have the right plan, rent for several nights not just 1, Friday to Monday is great. If you have no idea of floorplan or brand then doing it several times with a different trailer each time can help there.
If you want more trailer practice, then go rent a large uhaul for a day and find somewhere empty, it is hard to reverse a small trailer than a large one in my experience but the experience is transferable and will contribute towards the TT in the future at a much lower cost and timescale.