Les, if you're just gonna go down to the shops, then warm the engine up for a few seconds (I normally turn the engine on and then do up my shoe laces...).
Once you're there, since you haven't been on boost, you can switch it off straight away.
And, yup, the 1G-GTE boosts up nice and early because of the tiny turbos. Each turbo runs off three cylinders, so they both come on at the same time. It's not sequential like the 2JZ-GTE.