Using low-altitude platform stations (LAPSs) in the agricultural Internet of Things (IoT) enables the efficient and precise monitoring of vast and hard-to-reach areas, thereby enhancing crop management. By integrating edge computing servers into LAPSs, data can be processed directly at the edge in real time, significantly reducing latency and dependency on remote cloud servers. Motivated by these advancements, this paper explores the application of LAPSs and edge computing in the agricultural IoT. First, we introduce an LAPS-aided edge computing architecture for the agricultural IoT, in which each task is segmented into several interdependent subtasks for processing. Next, we formulate a total task processing delay minimization problem, taking into account constraints related to task dependency and priority, as well as equipment energy consumption. Then, by treating the task dependencies as directed acyclic graphs, a heuristic task processing algorithm with priority selection is developed to solve the formulated problem. Finally, the numerical results show that the proposed edge computing scheme outperforms state-of-the-art works and the local computing scheme in terms of the total task processing delay.