You don't have to resign at any point. Losing your queen isn't a reason to resign on its own. I resign when I can't see a way to avoid losing and I believe my opponent is very unlikely to blunder their win away.

If you want to play out the game then you should. I feel like you agree to play for the time on the clock, so if your opponent feels like they're wasting their time, then that's their own problem and not your fault.