Most courts resolve small cases like this within a year or two, including appeals. Indeed, a case that lasts more than 2 years is considered anomalous unless a huge corporation or very wealthy clients are involved.
It would take about 1 week to 10 days once appeals have resolved for the funds to work their way through the system. Every state has a deadline for paying off judgments. The only reason payment of a judgment would be delayed is if the defendant declared bankruptcy.