To my eyes, it's either 'New Dawn' or its sport-parent 'Dr. W. Van Fleet'. The difference would be that 'New Dawn' repeats while 'Dr. W. Van Fleet' doesn't. So don't despair about replacing the rose -- it'd be safer to start with a new one than to cross your fingers and hope that any cuttings that root won't be infected and spread the disease to your other roses.
You may want to spray the rose down with soapy water followed by miticide, so that any mites on it won't be shaken free to infect your other roses. If you're against miticides, just go with the soapy water -- use a hose-end sprayer with some dish soap and thoroughly soak the rose. Then start cutting it down. Next comes what to do with the removed rose -- if it's really large, you'll have to snip it up small and put it in a garbage bag to be picked up with regular trash. If you're in an area where you can burn it, that's even better. And if you're not, you could probably throw it piece by piece into a bbq grill.
But if I were you, I'd avoid temptation and go a year before you buy any new roses. You'll want to be sure that none of your others got infected but haven't shown symptoms yet -- otherwise, you'll end up having a repeating infection cycle going on in your garden. So watch any new growth on the others, and if by next Spring none have shown symptoms, proceed to expand your rose collection.
:-)
~Christopher
