If he's eating and breathing normally don't put him in QT. The stress of catching and moving the fish will only increase its susceptibility to the infection. Plus the only way to rid your system of ich is to let the system sit fallow with no potential hosts in the system for a minimum of 6 weeks. Your tang is NOT going to be happy in a bare bottom 10 gallon tank for 6 weeks, and if you don't let the system sit fallow, you're just putting the fish back in with the parasite anyway. Let the infection run its course, as long as the fish is healthy and eating well it will fight it off on its own. As all the LFS guys say, if you sneeze in the same room, a tang will get ich, the key is not to freak out about it. Keep soaking food in garlic, keep him well fed, and keep the parameters consistent - a raise in salinity or major change in temp or pH can worsen the infection.
If you do decide to put him in QT - do a 10g water change on your display tank and used the removed ("dirty") water to fill the new tank - do not put the fish in a new, un-aged batch of saltwater. The parameters are not likely to match and you'll stress the fish out even more and worsen the infection. Put some PVC pipes in there so the fish has some place to hide and watch your nitrate levels since you won't have live rock in there to provide filtration - you'll probably have to do frequent water changes.
But I wouldn't put him in QT. Just my 2c.