Private ceremony - do we need a rehearsal dinner?

You only need a rehearsal dinner if you are rehearsing the ceremony. Its purpose is to thank those who took time out of their schedules to rehearse with you. If you aren't rehearsing, then you don't need to have the dinner.

The rehearsal dinner is typically just for the people needed at the ceremony rehearsal, but you could always make the guest list bigger if you wanted to include more family member or out-of-town guests!

With that intimate of a group I think it's totally your call if you want to have a rehearsal dinner or not!!