There are legal questions that are specific to your location (which we don't know). I obviously won't address that but will answer as if you're in the US.
I'm going to differ with the other answers and tell you that you shouldn't quit until you have to go back and not before. If you give notice, it's very possible your company could refuse the notice and terminate you immediately. That would likely stop your health insurance as well as potentially your LTD since you're no longer working there.
Something else to consider. Since you've been able to look for work while you are disabled, it's possible that your employer (or their carrier) would allege that you weren't disabled after all and attempt to recover what you were paid while on LTD. And if you say that you couldn't do your regular job but could still look elsewhere, they could say that they weren't given the opportunity to place you on light duty.
One thing is certain though, you really need to find out what the legal ramifications are that are specific to your situation and we can't do that here.
If it were me, I'd actually return to work for 1 week and then give my notice. It makes everything cleaner.