If you are late people then I would suggest going at night on a Friday or Saturday. DQ is open until either 11 or 12 i believe on those 2 days. There aren't many people there at that time. I do it all the time. But to answer your question, i really do not have an answer because I don't know anything about the crowds on a sunday. sorry!
If the local schools are out, that could be bad news. This Oct. we noticed the crowd level pick up mid-afternoon, but then die down between 5 and 7. We really expected it to be busier as the day went on.