For me, all of my fish go through a copper treatment in QT before they go into the display tank. With that said, I don't think I would rush them into a QT environment under your current circumstances. You would be taking fish that are already very stressed and adding the stress caused by a move, a new tank, and potential cycling issues. That sounds like a recipe for multiple fatalities to me. This is what I would do if I was in your shoes:
1) Leaving the fish in their current tank and give them what they need to fight their way through the current outbreak. Keep them well fed with high quality food soaked in garlic and increase your water changes by 25% to improve the water quality.
2) While the fish are working on getting through the current ich outbreak, Put a foam filter in your sump. After about 2 weeks, it will be fully seeded with bacteria and ready to go in your QT tank. I use
this one.
3) Once the fish are through the current outbreak and the foam filter has been seeded for 2 weeks, move the filter and the fish to QT. Their stress level should be lower now.
4) Treat the QT tank with hypo or copper.
5) Run the display tank fallow (no fish) for at least 6 weeks to allow any remaining ICH in the tank to die off completely.
6) Move your ICH free fish back into your now ICH free tank.
7) Put a new foam filter in your sump so you are ready to set up your QT the next time you buy a new fish.
8) Never add another fish again without first putting him through hypo or Copper in QT.
Good luck!