We don't have any grandparents nearby and can't afford a sitter, so I had to start doing errands with DS when he was about six weeks old (he's 8mo now!) In the beginning, he used to get very sleepy in the carseat, but never transferred very well. So, I would do about 30min of errands before his naptime, then come home and immediately begin our wind-down. A couple times, he fell asleep fairly early into our errands, so I would take the time to do some more while he slept. It never affected his ability to sleep in his crib, so I didn't worry. Now, he's so interested in the world that he rarely falls asleep in his carseat, so I do errands with him as soon as he wakes up and eats.
I would encourage you to let your LO tell you what he needs. Also, I think most of us have begun to over-think things because we just want to do the best for our kids!