Well where you dial in your dot will determine when it will send rounds high or low. For an EDC gun I sight in at 10 yards. Then I shoot at the other ranges to see how this is reflected.
Also, I would say that from 0 to 10 or even 15 yards... sights are optional. Depending upon your skill level. Inside of 7 it really should be point and click. At least for just hitting COM on the fly.
When you say that you shoot one inch groups with irons, that's great. If you can't do that with a dot either your dot is busted and won't keep a tight zero or your dot isn't mounted tight. A quality dot is, in my experience, every bit as accurate as iron sights.
As to acquiring a dot quickly, I know that everyone is different. I think that when it comes to my dot acquisition it is probably something that an combat pistol instructor would look at and say:
So... I need iron sights to find my dot fast. I have put tall sights on everything (pistol) that has a dot. I just picked up taller sights for my CZ P-07 because I couldn't see them through the window of the dot. They are not co-witness sights, lower 1/3 but definitely there.
But I digress. Here is why I need tall iron sights in order to speed up my dot shot. I have been an iron sights shooter since I joined the military a thousand years ago (okay, since '94). For me starting the shooting cycle like I'm bringing up a non-dot equipped pistol is the closest thing I'm going to get to second nature. And I'm used to running qual/SWAT/Combat courses in this fashion. I'm wired for old-school. To make a dot work best for me means that my draw to aiming stroke hasn't changed. Having the sights just allows me to orient the pistol faster to where eye of sauron is floating over the front iron and I just transition from there to just the dot. I have tried to explain this to several of my co-workers. They just give the that look:
I have tried to just go to the dot. It only works about half the time. The rest of the time I feel like I'm looking for a ghost. So this is how I do. I really do like my dots and prefer them on my guns. On a string of fire, once I have the dot, I can keep it. I feel that they allow for more precise aiming (for me) and faster, extended range fire. But I do spend a lot of time to ensure that they are spot on accurate (to me).