There is the 1820 Society. Unlike the other clubs onboard, it's more participant driven. They typically meet the first night of a cruise with a CM who will facilitate any activities the group wants to set up.
If no one shows up at that first, organizational meeting (or only 2 or 3 do) the club may not get off the ground.
Our son enjoyed his cruise at 19 with the group, but they had a fairly large group (15-18 people) and they planned a lot of stuff.
All that said, a 20 year old can participate in any of the adult activities onboard (except alcoholic drinks), so there's that.