I think a 120 is fine for a rock beauty, they only get to 10 inches in the wild and usually under 8. It is illegal to take them over 5 inches in Florida waters and in fish tanks most are not full sized, besides except for pygmy angels most of the full sized angels can get much larger even in fish tanks, I have seen queens and blues over 2 ft long in the wild.
While I agree you should qt your fish most rock beauties will not even try to eat prepared foods unless they see other fish eating it. I have collected hundreds of them when I was working as a commercial collector and we always put them in a tank with fish that were feeding well from the first day. While I agree with Sandwi54 that qt is one of the most important things you can do to prevent disease in your main tank I don't agree that it is less stressful on you animals. Catching the fish out of qt and moving it a second time is a very stressful event for a fish. Also having a fish in qt where it is uncomfortable because of very little hiding places so you can observe it and keep the tank clean of uneaten foods is hard on them as well. If it were my fish I would put it in qt with live rock and with other peaceful fish that were feeding well and acclimated, this way they are not shy, giving the rock beauty the feeling that it is safe and showing it what prepared foods are. The other choice is to put it directly into the main tank and the problem with this is that without qt there is a very real and serious risk of introducing something to your main tank and that is something you can not take lightly.