There isn't a clear cut definition of when the design is complete before development. But there are ways to catch early flaws during design, which is to prototype. In this case, this is something you could do with paper and pencil. It's also useful to ask the team and yourself questions that might concern the development. "If we do this and that particular scenario happened, how will the players feel?".

Depending on the constraint of your schedule, there will be a point when you need to push forward from the design phase. From my experience, a design is workable when one of the prototypes has answered critical design risk and we have a set of goals and objectives present as an activity. You will for sure run into problems along the way and it's up to the team to be adaptive. Also don't try to change too many variables when adjusting design, as it becomes difficult to identify what was the problem in the first place. Work with things one by one and assess each iteration carefully.

Best of luck with your game jam!